Suggestions for day out in London with children who don't know each other?

[Shufflebumnessie]

I'm looking for ideas of where to head for a day out in London, it'll be a Saturday in either April, May or early June.
My second cousin wants to meet up so the children can meet each other. We don't really know each other and haven't seen each other in over a decade. Family 1 - 2 adults & 2 children (aged 13 & 8), family 2 - 2 adults & 1 child (aged 11).
Neither of us live in the London area so we only ever visit as tourists.
Is there anywhere that you can think that we should head to where the children will enjoy, and the adults can sit & catch up?
Ideally somewhere that will keep the children entertained and will appeal to all interests. We'll probably also have lunch and/or dinner with them too.
Just to add, the 13 year old is very young for their age and still enjoys large playgrounds etc.
Thanks in advance.

Natural history museum.

The Diana memorial playground is good if the weather is nice. Science museum is good. My 11 year old still loves the wonderlab bit but might be a bit young for the 13 year old. Postal museum is really interesting but quite small so won't fill a full day.

Graffiti tunnel (with some spray paint cans)

One of the indoor crazy golf places like Puttshack

The Olympic park in stratford.

I haven't done it myself but a friend recently did life-size Monopoly with DC's aged 11 and 14 and they all loved it. Worth checking if it's suitable for the youngest.

We did an 11th birthday party at the Crystal Maze which all of the kids enjoyed - great way to get them all working together.

Sorry, strike that, aged 9 and over! Should have checked before I posted

Both adults here with no children but we were in London recently and went to the F1 Arcade(F1 simulators - think arcade game but way better) - it was huge fun and there were several children there too. as we don't have children I'm not sure on ages but there were probably ones in your age range there too

There's different packages, we did the 45 minute one - you can choose from 5 different difficulty levels but all still race together. The seat etc move.

If they're into F1/arcade/racing games would be an option and something for them to chat about after. I wouldn't go to London just for that as it doesn't fill enough of the day, but would be fun activity for part of it depending on what the children are interested in

National history museum?
Science museum?

Thank you all so much for the suggestions, I knew there'd be some great ideas.