I don’t live in London, and live rurally , but rarely spend money on stuff to do. Here are my tips:
I buy one annual pass a year. There’s a zoo/ farm park near me (1hr away by car) that has loads of parks (climbing frames etc ) and a softplay. It’s 100 quid a year for me and the little one and you can do stuff there come rain or shine. I’ve done this a couple of years in a row, but this year I’m getting an aquarium pass as he’s mad on fish. Then we can go whenever we want. You could also do this for a softplay or similar .
we also do lots of walking - I have an OS map subscription and we have various purposes for the walks - collecting sticks or leaves for crafting, bird watching with his kiddy binoculars, taking pics of different mushrooms etc. we take a ‘picnic’ with us (just a sandwich and fruit) and stop somewhere half way .
we go on ‘bike rides’ where we take his little bike to nearby parks and cycle (and I walk or run) for ages. We also take a ‘picnic’ and some drawing .
we fill a bag up with toys and take them to the park when the weather is nice. Sometimes we take the wooden brio track and he can play with this for hours. I have a little pop up tent (free on Facebook marketplace ) which is great for getting some shade.
we aren’t far from the beach, so in my car boot I always have the ‘beach kit’ which consists of buckets, spades, towels, blankets, a kite etc. we can usually get half to a full day, depending on weather (I got the beach kit from various car boot sales)
I also bought little rain trousers that go over his wellies( also from a car boot) so when it rains we often go puddle jumping. We also go to the beach when it rains and he enjoys playing in the sand just as much.
local (council run) pools often have free swimming times for under 16s. I have a subscription that covers all council pools in my county, so we bounce around from one pool to another taking advantage of the free sessions for tiny. We manage to get 2-4 free swing sessions a week.
Also council run leisure centres often put on free holiday time activities. Our closest leisure centre does free bouncy castle sessions in the hall or messy play as well as things like ‘football camps’.
play dates are always entertaining- last summer myself and my kids best mates parents organised to see each other every Wednesday. We would just meet in the play park and could get 3-5 hours out of that .
if I lived nearer museums, I’d be visiting at least one a week. In London, you’ve got the natural history museum, science museum etc which are free. Even for the little one, it’s entertaining. Take a packed lunch and have a rest in the garden/ on the steps after.
i then alternate ‘going out’ days with staying in days. My son knows what is happening next and it allows me to get housework done. I do toy rotation, so he can get a whole day of play out of his toys. I also get him involved in organising/ tidying his room at the end of the day - it takes up tons of time 😂
I manage to survive on no pay over the summer and I earn about min wage the rest of the year. It’s tough, but you can have a nice fun summer without spending too much . I dreaded the first summer my little one was 3 because I had no idea how I was going to keep him busy. Now I look forward to it. I do have only one kid though 😂