Just a small correction, it is the Museum of London at the Barbican, not the London Museum but it is free and v.interesting - lots there if you have children doing about the Great Fire of London at School. Maritime Museum and Observatory at Greenwich aren't free.
Fond memories of that, is it still there? I recall that when we visited Ambeley Museum a few years ago the younger Pottings were fascinated by the phone exhibit particularly the dialling.