Also in the southeast and don't drive so these are all accessible by public transport.And very tight budget. Mine are older but these have been firm favourites for several years.
Kew Gardens - fantastic day out, so much to do we go several times a year. Sensory childrens garden gets very busy but plenty of other climbing and things to do. £2 if you claim universal credit or other benefits. Also on the 2 for 1 days out on the train.
London zoo - again we go yearly. Play area aswell as lots of animals. Penguins are fantastic and loads of seats so you can watch them while u have a picnic! £5 on universal credit or 2 for 1 days out on the train.
Various free London museums - the war museum (great as has a big play park next to it so can take outside run around breaks!) Usually activities on in school holidays. The V&A. The natural history. The science museum. The British museum.
The london transport museum was great for kids mine were a bit old at 11 and 14 but still enjoyed it. £1 for an annual pass if u get universal credit, kids are free.
Portsmouth dockyard. We did annual passes from groupon for several years running. We went every holidays, saw different boats and did all the interactive activities.
Tower of London was brilliant fun - tip go straight to the Crown jewels it gets busier as the day goes on. And do one of the tours they are fun and informative. Better to go not in the summer as its quieter in the half terms/winter. £1 on universal credit.
If you are near Brighton we love a day at the seaside. 2p machines on the pier. They sometimes do deals on the wristbands for rides. You also have Hollywood bowling who often do 50% off before 11am in holidays and globalls. Look out for deals for the Royal pavilion or sealife centre.
Paradise Park in Newhaven. We went several times a year until recently as mine are now too old. We used clubcard vouchers.
Various castles We did on clubcard vouchers/discount days. Best was Lewis and Arundel.
Arundel wetlands centre is lovely, not too busy but lots of playareas for kids too. Can't remember price of this.
Meerkat rewards are your friend for days out - 50% off at pizza hut and various other restaurants. 2 for 1 cinema tickets. You can get a year by doing a 1 day travel insurance for around £1.20. Family of 4 do 2 accounts for cinema. Just book at the same time to get seats together.
Research lots of different parks a bus/train ride away. A different park is always fun at that age. We went to a great ones in Chichester!
A day in Littlehampton- sandy beaches. Harbour Park rides/arcade. Lake for crabbing. You buy bait bags in the little shop nearby. Also insanely cheap ice creams. I got 2 Mr whippy with sprinkles/flake, vegan magnum and a tea for under £5.
We went to gullivers (in the car not doable on public transport) and stayed over. It was really reasonably priced, loads of rides and the longest we queued all day was 15 mins. Highly recommend it for those who don't like big rides or younger children.
We've done the big days too legoland and Chessington - both I recommend downloading the app and going back and forth where there's no queues. We did this middle of August on a sunny day and didn't queue longer than 30 mins at legoland. We went on everything too, dd2 went on the little dragon ride about 10 times plus loads of others!