Re: What's a sailor to do in London?
Greenwich, Portsmouth, St Katherine's Docks (and the Tower) - all great 'salty' destinations. The former two are day trips.
In Greenwich, remember to visit the Prime Meridian, to stand on both the east and west of the planet. The clocks are awesome (read Sobel's book Longitude first!)
Portsmouth will take a sailor a while. In addition to the Victory, have a look at HMS Warrior - the ultimate hi-tech battleship. Sadly never used in actual combat, as she was so advanced any aggressor just gave up on the spot, or ran away.....
It's always interesting to compare two great ships - the USS Constitution and HMS Victory. Old Ironsides was built in 1797. and was a 44-gun frigate. the Victory was built in 1778, and was a 104-gun first rater. However, tragically, some dimwit decided to keep the Victory in drydock - a tragic thing to do to a wooden vessel. She should be afloat, like the Constitution.
Plenty more suggestions available on request.
(Disclaimer: I am a Londoner born and bred, and have an absolute conviction that it is still the greatest city on Earth - and I have seen quite a few other of the world's 'greatest' cities. Totally objective, of course!)