You can do things very cheaply in London if you look hard enough. For example you can bay a return ticket on the river cruisers in the summer for about ?10. Get on at Westminster or Waterloo and go out to Greenwich. You can even stop off at the Tower of London to have look around the outside and get back on. At Greenwich visit the observatory and meridian (free). Have a picnic in the park.

Museums are still mostly free and many of them have been updated since most peopel went as children. The Imperial War museum is very interesting, particularly the WW1 experience. Plus of course all those on Exhibition Road leading up to the Albert Hall, and Memeorial, which is spectacular.

The royal parks are also a very pleasant way to spend a half day or so. If you plan tour route you can walk from Hyde Park to Trafalgar Square with very few visits to concrete.

Hampstead heath and Hampstead itself, with its village feel and shops is also very pleasant