That's pretty tight. I think you could probably do airfare and lodging for that price without too much problem, but to make room in your budget for meals etc you'd probably be looking at renting an apt a bit outside of central London, with a good transit option into the city.
Generally my rule of thumb is that prices in London are what you might expect in DC or NY, except for being in pounds not dollars-- so everything is about 2/3 more expensive now.