I spent 8 days in England on business, primarily in London and then a return trip with a day of sight seeing in London.
One recommendation. The bus tours cover all of the major areas of London. If I remember there is a Red, Yellow, and Blue tour, but they overlap and you can transfer from one route to the other all on the same ticket. Hope for a nice day and ride on top in the open air. For an extra few pounds you can add a one hour boat tour on the Thames. From taking the bus tour I then went back to the Tower of London (the Crown Jewels). Get there when is opens and take the tour conducted by the Yeoman Warders - very entertaining.
If you like the theatre, London is much cheaper than NY, Broadway. Its the only thing that I found to be cheaper.
I was there in late Sept/Oct and then back in mid Nov. We had rain, drizzle, sun, warm-humid, cool-damp. Good luck and have fun planning. Some day I hope to return with my wife.
PS. Buy a guide book of London before you go.