London with kids

When mine were small they loved the Science Museum.

Just to add, they will love Tower Bridge, and if you sit and eat your sandwiches by the river then they might be lucky enough to see it open.

Personally I would try and show them some London sights rather than playing in a park which they could do anywhere. But agree the foot slog could be too much, so an open air bus ride would be perfect and you can point out various famous buildings from the top deck.

If walking then try and see some horse guards. These are London things they will remember The Kings Life Guard

I would save the Tower of London for when they're older. It is very big and hard work, with lots of things they won't understand. Just too much for young children.

A boat trip to Greenwich- there is the Cutty Sark and the maritime museum, the park is lovely with a good playground.
You can book free tickets to the Sky Garden which gives great views over London, but book in advance.
The V and A has a lovely courtyard with little paddling pool where you can sit and have lunch. Somerset House has water fountains which the kids can run around in while you sit and have a coffee- (take a towel) the Southbank has similar fountains. Somerset House currently has a Cute exhibition with lots of Hello Kitty themed items.
The Horniman museum in Forest Hill ( train from London Bridge) has a butterfly house, little aquarium and currently a small dinosaur exhibition, very child friendly with lovely gardens.
Young V and A is worth a visit- lots of activities for little ones.

I agree that a tourist bus would be fun or a boat ride on the Thames . I did both these with mine and it saved much foot slog.

There is a park in London which you can only go into if you have children with you coramsfields.org/
It is close to the Foundling Museum, but I think your children are a bit young for that foundlingmuseum.org.uk/

When my children were small we used to go to Princess Diana's memorial garden. It was brilliant a peter pan themed park which is all gated, the children can run and play safely while you relax

A bus ride?

London Aquarium, and a stroll along the South Bank which has various child friendly attractions along with the London Eye.

The Tower of London is also child friendly along with the many parks.