Five days is too little, and the airfare you list is too much. Get a cheaper flight, perhaps at a different time, and stay longer. You'll regret doing the fast, racing tour, that so many Americans seem prone to doing.

England has so many lovely spots, but one close to London, within reach of the airport, is the Cottswolds. I'm partial to fishing villages from Cornwall to Kerry, to Donegal, to the western highlands, and all around. It really depends what you like to do. We like to walk the public right-of-way paths, and Stately Homes bore me. For you it may be the opposite. Give us some clues!