If you're in and around the capital, get an Oyster Card; It'll save you loads of time and money on the public transport (which is some of the best in the world). Needs a deposit of £3-£5 , I don't remember which, to buy one, and when you're done you can return it for the full amount (or keep it as a souvenir).
Just...one thing. If you're coming out of the tube? At the top of the escalators? Don't fucking stop dead to find your ticket/Oyster - either have it ready or move to one side, else everybody will want to stab you.
In fact, if you have it to hand, you shouldn't need to stop or even break stride - just tap the card on the reader and you're done.
Don't forget that most of the museums with the word British or Imperial in the name are free; The British Museum (also called the Imperial Museum) has the largest collection in the world and is completely free; We even pinched the marble off the front of the Pantheon. The Imperial War Museum and the British Science Museum are also free.
What dates are you around between?