Milton Keynes?
OK so I know it's not the most obvious place to head for but in October you're not going to be wanting things like beaches and sunshine stuff...
It has:
Gulliver's World - Theme park that's aimed at younger kids (not sure how old your eldest is), also includes a Dinosaur Park, a petting farm, a splash zone, a nerf gun battle zone and more.
Sporty stuff - indoor ski slope, indoor sky diving, Go Ape, Zip Wire over the lake, Pirate themed crazy golf, ice skating
Couple of big soft play centres
Cinemas - big cinemas including UK/Europe's first interactive 4d one and first Kids screen (has soft play stuff up at the front for the kids while you get to sit on your seat in comfort...)
One of the best theatres outside London
Woburn Safari Park (albeit half of it is a walk around zoo and half is a drive around one so you'd want to be in a car - unless you can run fast enough to outrun the lions
Some lovely parks and woods with visitor centres/tea rooms etc and if half term many of them will be running free half day play sessions with free bouncy castle, craft stuff, play leaders organising games/etc thanks to MK Play
History - from Bletchley Park to the Museum of National Computing (the latter usually runs holiday afternoon sessions, the ones recently have been for all ages as there's always loads of lego out, more advanced lego mindstorms, computer games from through the ages and different themes from things like K9 visiting and his maker to talk about special effects in Doctor Who, computer music, etc. There's Roman remains (yes, I know everybody thinks it's a new town! But the original MK village has been here for a very long time and there were settlements around for a long time before that). Stowe is nearby, a big National Trust property with lovely grounds.
MK Museum - award winning museum that's really hands on and great for kids - an old victorian farm house where you can play parlour games, make your own toast on the range, sit in a victorian school room, see historic toys, a street of olde worlde shops and workshops you can wander through, similar but for farming tools and stuff, a phone museum section (sounds boring but is actually lots of fun and difficult to get kids out of), a transport museum section with lots of old vehicles that you can get into, and more. And a nice tea room and shop.
The concrete cows
Emberton Country Park (not so good if it's wet or cold - but otherwise a big fantastic park you could spend a day at)
Thrift Farm - small petting farm with nice cafe, aimed at youngsters (There are other visiting farms nearby that are bigger but probably also would need a car to get to).
MK Gallery - great art gallery that always runs lots of kids' art sessions during the holidays
Plenty of restaurants and shops and normal city things too!
best of all - if you get a fast train - it's only half an hour from Euston.