To wonder what to do with my children on these endless rainy afternoons?

It sounds extreme but I would really strongly recommend swapping your days off so that you are at home at the same time as your friends.

I do feel your pain, I like to get out of the house even for my own sanity - our days fully at home are very limited as I just go a bit stir crazy

Did a quick search for library's in East Midlands (obviously it's a fairly big place but you can look up the ones nearest to you) and clicked on one at random (Kettering) which has things for under 5 year olds on Mondays, Tuesdays, Thursdays and Fridays. Granted the event itself (story time, play and learn etc) is only an hour but you can join a library for free, let the kids enjoy the hour with other kids, then pick a couple of books each and return the last ones.

Other things...

Castle? Talk about princesses and princes and knights etc, explore the castle, enjoy the grounds when the rain lets off and indoors when it doesn't. A lot of them have a nearby cafe or one inside the grounds

Pottery place? Some of them offer messy play which you can attend more regularly where a few kids go and just do painting etc which is quite fun. The pottery itself you probably wouldn't want to do more than about once a year (handprints or whatever) but worth checking if they do some other craft related activities for kiddos

Indoor mini golf? Some are very interactive, the young one can crawl about and the older one have a go and watch you playing it. I never did this with 2 of them just with my one child since he was about 3 or 3.5 and he loved giving it a go - recommend doing that in term time during school hours so there's only really younger kids who don't know what they're doing and no one's very annoyed if you just spend ages on one bit

I think they do under five sessions at trampoline centres and ice rinks too where parents are on with them - but I never tried those myself, probably under 1 is too young for those though the 3 year old would be okay

Museums - if it's interactive and interesting, like cars/trains/science/animals - not the history/artsy ones

Cinema - totally depends on the child but if it was a short childrens film mine would love that, I normally did M4J so that it's only £1.50 per child and same for adults - doesn't feel too painful if you leave before the end. Most cinemas have ride on cars just outside and an arcade somewhere within the area, plus some food outlets so it can burn through quite a bit of time just 'seeing a movie'... I swear mine only really asked for cinema because he wanted the arcade 🤣

Looking just now the national space centre Near East Midlands looks really cool! Mine would have loved something like that :)

Sometimes even just going to an area which has some interesting shops works for kids - e.g. aquarium that sells fish to go see them bobbing about, a shop you might actually want to go in, then pet shop to go see the rabbits etc, then another shop you want to go in, finished off with some food or whatever

National heritage sites have stately homes and sometimes a little park and somewhere to eat, park as and when the rain stops...

There was a local garden center near one location we lived - we couldn't get there - but they had petting zoo, play area and a cafe - it was very popular at Christmas as they did a grotto area.

Another location - again we couldn't get there - but big country house did some activities round Christmas and other mothers who had car access drove there and did those.

It really does depend how mobile you are and what's around

https://www.dayoutwiththekids.co.uk/things-to-do/east-midlands

I'd look at these kind of sites and see if there's local stuff you've missed.

Though few summers I did in one are we live just pack a lunch pick a dry day and go round all the small local parks before ending up in central large one - but weather has to play ball.

I've been there, totally feel your pain!
I live in the north west and it rains all the time.
I'm exhausted from thinking of how to entertain children... but maybe that's the problem. Maybe we need to just accept doing nothing is also fine! I think we demonise TV and screens when they can actually be really helpful. How about dinner and then a couple hours quiet with the tv or whatever and then a walk or whatever after.
I know it doesn't sound exciting... but I guess I'm suggesting just trying to let yourself be settled doing nothing too!

We used to do morning at toddler groups and own toys/craft baking/sleep/help me with chores bit TV in afternoons/music/long book reading sessions - really bad days sometimes long baths.

However sometimes you do need to get out - any afternoon groups - local museums - even local art galleries - walks and cafe - walk and library - any toddler/baby afternoon cinema sessions near you - walk to local shop with list and money. As many PP have said if you are near visitor attraction who do 12 month tickets things - then those - I mainly saved those for weekends when extra pair of adult hands.

Dd was and still is a sucker for a sticker book, jigsaws, craft type things (you can leave them with some pritstick and bits to stick onto stuff quite happily). DD liked acting out stories (but this is very painful for me), the best one was where I read out room on the broom while she pretended to be the witch. Making a fort for her stuffed toys was another favourite. Bath time with blowing bubbles.

Can you get a farm park/ zoo membership? Matlock farm park is nice. What about forest school type groups if you want to get out of the house a bit more?

I also buy bulk loads of clearance craft stuff from Baker Ross/ The Works etc and save it for rainy afternoons.

Get your paper and pens out and let the older one draw a card/letter. Let the baby have a scribble on a piece of paper too.

Then go on a walk to find a post office, buy a stamp, then walk to find a post box to post your letter to granny/yourself.

Library?

Whereabouts roughly in the country are you? Maybe people can help with specific ideas then!

I get what you mean. I have a limit on how much indoor stuff I can tolerate, especially when 75% of it is breaking up arguments and clearing up mess 😂

Mine were this age as we came out of lockdown. Once the rules were relaxed more and you could browse, I used to take mine to The Range, Home Bargains 😂 anywhere! You can point out all of the different colour cushions... my older one loved the mirrors.

I get your youngest might need to be in the pushchair but could go front facing in a sling to give them a better view? Then a cafe for a cup of tea and a biscuit?

I don't know if you're anywhere near bluewater or lakeside (any shopping centre will do) but mine also liked walking round there (during the day when it's quiet). They often have small play areas dotted around, bluewater does have a nature trail too, if it rains hard you can come back indoors.

I know it sounds sad but these kinds of days put kept me sane after PND and covid etc.

+1000

Then all three of you would have proper mental stimulation all day.

Mine would play keepy-uppy with a balloon for a surprisingly long time at that age. Good if you only have a small garden or inside if it’s really wet.

You can also make an obstacle course by stringing wool across a corridor. Quick to set up, baby can crawl along the floor and the older one can practise ninja skills by climbing over/under the wool.

How wet is it? Mine used to like feeding the ducks and puddle stomping and I found it bearable if we dried off in the nature reserve cafe afterwards. It’s easier when they’ll still wear all in one suits because then it’s just yourself you need to keep dry.

Cosmic kids yoga is really good too. Project it onto your tv and pretend you’re out at a baby class!

Transport day - go for a ride on a bus/tram/train. Costs a, day rover for you and free for the children. Don't have to go anywhere in particular, but a cafe stop, or interesting large shop, or museum or art gallery en route can be good. Can spend a while in a train station watching the trains. Make the travel longer than direct a-b, and the excitement.

Walk to the local shops to buy ingredient for tea - again walk the long way round. Stick in bath afterwards to warm up if its wet and rainy. Take yourself a mug of tea into the bathroom so you can recharge a bit while they splash.

If it is just drizzly do go to the park in waterproofs. Take a flask/keep cup of tea/coffee with you - hot drink is how I found standing pushing a swing in the cold to be bearable.

See if you can befriend another family or two with similar age children.... Meeting up at a park in the rain is much more bearable with another adult to chat to, and taking it in turns to host for an hour or 2 at home for a cuppa while the children play can fill part of an afternoon really well... You could bake buns to eat when friend comes round as an indoor activity too.

Filling the days when the weather is rubbish and the kids are small can be really hard work, I remember it well

This and also public transport to get there can be fun and fills the day

Have theme days, so Pizza day for example - Do a list with simple pictures for the 3yr old to follow and take them shopping for the ingredients (sainsburys do a dry dough mix you just add water to I would recommend and supermarkets where they have the mini trolleys, give the kids the money to pay with) then you go home and make the pizza, wear aprons, play opera music etc, this then also serves as lunch and really does waste a few hours and is teaching them social skills, forward planning as well as basic cooking.

Get a toy rechargeable remote control car, 3yr old will love it and the 11mnth old will chase it around - this one we have is indestructible! You can build ramps/obstacles etc. https://www.googleadservices.com/pagead/aclk?sa=L&ai=DChcSEwjR8fL67dCGAxVyklAGHVlJAikYABAYGgJkZw&gclid=CjwKCAjwyJqzBhBaEiwAWDRJVBEE0D4UcqeougwftzdrsG0yzPVnfutrpEm6cLnkVFkEpoj32N_NBBoCSNAQAvD_BwE&sph=&ohost=www.google.co.uk&cid=CAESeOD2WoorlJRN9sBgLiPmrrD_HJL9j6rc212plVcAcDRP60jOpl7_Dqe_js9AW13w5s77E8ue3A5sphkk5eacp1FtNmAgwGB5kBNIADGiID2xvLyGiVvKvQX5GHuOZmRYpYfL8xGEaeTwiAWiZd0tZZksPIP76tiENw&sig=AOD64_2w4DHuG2S3qPxOGjs_P5hS0Z7B6Q&ctype=46&q=&ved=2ahUKEwirpev67dCGAxXRQ0EAHQJUDlsQzzkoAHoECAYQOQ&adurl=

Final one, is to do the you tube dance/ninja videos for kids where they copy the actions - I know its TV but it’s also exercise! I learnt mine liked it when they used to try and get involved with my exercise and yoga videos…which are also an option as gets you moving too.

Museums
wildlife trust places (they do toddler days which are fantastic)
zoo membership
National trust places
shopping when they make lists - draw pictures of fruit and veg.
aquarium and aquatic shops (Maidenhead aquatics let you feed the fish for £1)
libraries

best thing I ever did was buy a puddle jumping suit and just get out in it.

I had two 17 months apart so I remember this stage.
I would do the group in the morning then back for lunch and hopefully someone would nap.
Then the afternoon we'd usually go for a walk with the double pushchair either to around about or to the shops or I'd get a take away coffee. I know it sounds dull, but usually someone might have a snooze (not me!) and it killed a bit of time then back for tv and tea time. Or I would go to someone's house for a play or vice versa. It is a boring phase, I won't lie.

Mine loved a trip to the supermarket at that age. Ride in the trolley, give the eldest the list and get them to help. Even better if you have one near you where you can scan the items as you go round. My DC love this.

Similarly trips to Ikea, Decathlon and Pets at Home are popular.

Any nice local museums near you? I've found even the smallest and most improbable museum can keep mine entertained.

Oh I remember those days very well! There are only so many times you can go round the park in the rain. Museums and garden centres are a good shout, my two loved wandering round a garden centre. It might not be possible near you, but any pick your own farms opened yet? Where I am pick your own strawberries are usually in a polytunnel so actually not horrific even in the rain.

Even an art gallery can be a distraction, usually lots of rooms to run through - and some galleries here have free activities for kids which offers a distraction. Plus of course ikea can easy fill an afternoon if there's one near you.

I used to take mine to the pet shop sometimes to look at the guinea pigs. Anything to get out of the house.

Do you have family around OP like your parents who might be not working. I would go and visit them :)

a cardboard box with every plastic sieve ,funnel ,microwave container,spoon and lid you possess to be opened up and laid out and then stacked and replaced. Bubbles are a godsend blown by you for chasing in the house and catching. I loved packet bought crumble which could be stirred round in plastic bowl with spoon for ages. Bake an apple in the microwave add the topping and it’s a treat for daddy when home😀 I had ready made rolled out pastry as a stand by and cut out letters and a plastic lattice cutter which could be given for poking out the holes. Gave me time to clear up.
I also crochet and found that just sitting there with them rolling around on the floor at my feet they chuntered away happily. Much better tv for kids now as I’m a G’ma to several.

Try trips to big, boring shops like DFS. Usually carpeted, so baby can try to stand without too much to hurt themselves. You can kid yourself it’s educational by doing a bit of half arsed “can you find a red chair?” with the toddler too. It’s quite boring but free, dry and warm. Curry’s is always good for toddlers too as they like opening and closing the doors of washing machines and the like. Pets at Home is the best but save that for special occasions.