Loads of places to go for free museums; churches etc, check out costs before you go. Costs nothing to have a pic with a policeman, soldier etc.
A place to see real history is to walk round historic areas for free. The walk on this link should not disappoint, it covers a lot of architecture used in historical films. Don't be confused by the name Temple, it is a legal not religious term here! http://www.londontourist.org/walk%20three.html
Loads of places to sit and eat a picnic so buy sandwiches for lunch, Marks and Spencer + Pret a Manger are excellent quality.
Ask for tap water in restaurants and if you are not too hungry just have a starter and dessert for dinner, stand for no nonsense from waiters, you are paying! Won Kei at 41 Wardour Street, London is a MUST, very reasonable as are many of the other Chinatown eateries.
Another place I have eaten superbly well is Bistro 1, 75 Beak Street in Soho. A modest establishment with friendly staff and the very best value, http://www.bistro1.co.uk/
Buy tickets for shows at the official booth in Leicester square for later in the day, huge discounts. Beware of fakes offering so called discounts to the unwary.
Plan to see London area by area, its quite big and time can be wasted if you don't appreciate this. A little planning will save loads of time.

