Matt: Also two blocks (or less; turn left as you leave the hotel, on the same side of the street) from the Kensington Hilton is Roberson's wine store - one of the best in London, if not the world. For my money, it's more fun than the Safeway.
And, if you want to recover from the pub crawl, check out their treadmill and exercise bike with the computer-driven displays. You race against a competitor who adapts to your speed and always passes you, but by a small enough margin that you can pass him with a little more effort, after which he will pass you again ... truly diabolical!