I don't know your age, but if you are a Beatles fan, Liverpool is a 3 hour train ride from London. The Liverpool train station is a nice 10 minute walk (all downhill!) to the Mersey River where there is a nice Beatles museum and then you can take the "Magical Mystery Tour" bus ride and see where all 4 lived as kids and adults, Strawberry Fields, Penny Lane, etc and the bus drops you off downtown at the new Cavern Club. The bus drivers and tour guides grew up in Liverpool with the Beatles, same schools, were in unsuccessful bands and had great stories to tell.
Liverpool had declined in the 70's and 80's but the downtown and riverfront areas have been redeveloped and are very nice- safe and pedestrian friendly.
Stratford on Avon is a real tourist trap and not recommended. Oxford University was great, lots of history and architecture. Warwick Castle is a 20 to 30 minute drive from Oxford and is also worth a 3 hour visit. It is owned by the Madame Tussouds (sp?) company but they do a nice job of it.
Bath and Stonehenge are great. Kew Gardens in London are fantastic and you can get there by train. The London Eye is wonderful on a good weather day and very close to the reconstructed Globe Theater. The Globe was much better than Stratford on Avon.
If you are a history fan or WWII buff, the Churchill War Rooms are not to be missed.
Edinburgh Scotland is worth a trip and I recommend flying there from London. The Castle (especially the POW section where American Sailors were imprisoned during the American Revolution), the Royal Mile and ,at the foot of the Castle, the Scotch Whisky Heritage center is informative if you like the beverage.
We went back to London in August just to take the Buckingham Palace tour. Her Majesty spends August and September in Scotland and therefore Buckingham Palace is open for tours. Well worth it and puts our White House to shame by comparision.
Another suggestion that will sound completely bonkers- The west coast of England (Cornwall and vicinty) is a wonderful beach vacation spot. The Gulf Stream is there and it is the warm part of England.
Bon Voyage!