BarbaraOfSeville
London as the Capital has many, many if the big museums and galleries, as national institutions, funded by the DCMS via the Arts Council. Natural History / Science /V&A / Museum of London (funded by City of London), Museum of Docklands (ditto) Maritime at Greenwich, Astronomy (at Greenwich), Museum of Childhood, local museums such as the Hornimann, the galleries (Tate Modern esp good for kids). The South Bank Centre has free events every single weekend.
So, everything available to visitors is available to Londoners every weekend. In addition all the big cultural institutions run regular classes and courses: music, drama, art, you can find classes and clubs free or very cheap (drama, £2 a session).
People say London is crowded: it is, with international visitors bringing in their money for world class culture, and UK visitors, enjoying their Capital for a day or so. Most Londoners I know welcome visitors and enjoy tne privelige of access to tne Arts and culture that atttescts them.
London is, I think, the only net contributor to the economy.
As a PP said, the free fares for children (free on all transport til 10, then free on buses, child rate on tubes) is paid for by the GLA from monies contributed via our council taxes and other specific London revenue. But visitors are extended the same privelige.
Lobby your County or City Council, and encourage them to adopt an integrated all-transport contactless payment system while they are at it 