There are bits of the museums that are really quiet. I went in the middle of August to the natural history and science museum with my nieces last year and I asked the guards which bits were the quietest.
I go the V and A most weeks and often I'm
the only person in that bit - I had the whole jewellery section to myself for an hour.
So go and do an hour in a quiet bit then walk back to Venchi and buy an ice cream and go for a walk in the park.
We went to Hyde Park last weekend and there were thousands of people but there's still plenty of space for picnics on a blanket, places to feed (proper seed) to the swans plus the Diana memorial fountain - yes it was busy but you're not queuing to splash your toddlers feet or anything.
A walk down the south bank yields the huge sandpit/ beach bits in summer plus the actual beach bit you can (scarily) climb down to. You can get food at the food market behind the royal festival hall or the children's plate in the cafe in the national is £4.95 - I spent all summer eating that (home made fish goujons and chips). Pizza van outside the national does whole pizzas.
There's also a very cheap van if you're on a budget that does 10 mini doughnuts for £2 or doughnuts, chips and a drink for a fiver.
Southwark cathedral is free. St. Paul's do a service every day at 5, it's free to go.
2 gardens in the sky to recommend - both free - the sky garden in Fenchurch street and another at 120 Fenchurch street. Both lovely - I actually prefer the second one to the sky garden as it's more open.
Don't underestimate the fun of going to places like Waterloo station for a coffee and a juice to look at the trains and shops if she's little. My niece thought that was her favourite bit of the trip
when she stayed with me.
And the farms are free - mudchute city farm and the one at Surrey quays I've not been to. Loads of animals to feed, plenty of places to picnic.
River trip on the Thames clippers down to Greenwich where I live - masses to do for free here. You don't need to pay to go on the cutty sark - you can just walk round it and take photos. Plus there's bits of the observatory that are free - the displays bit on the left around the cafe in the planetarium - only the museum and plantarium shows are chargeable. The national maritime museum has a whole kids bit that I unfortunately spent way too much time in last summer with all my visitors.
Bored writing now 