I would hit the tourist sights. Tower of London was worth my time due to the historical significance. Take a Beefeater tour, they are former military and very entertaining. Westminster Abbey, Buckingham, St. Pauls Cathedral, and the Changing of the Guard all were worth my time.
If you are looking for ideas beyond those, check out the London gunshops. Holland and Holland, Purdy, Beretta, William and Son all are in the downtown area. I found the men at Purdy to be very informative and helpful. They showed me their gunroom and let me handle guns I will never have a chance to again. Also, I had one of their "gun guys" fit me for a shotgun so I know what fits me.
ddj
I'll second ddj. Having spent a number of years in the UK while in the USAF, seems everyone wanted to come and visit - and tour London. It was my experience that booking a tour that encompassed as many of the sights as possible in a day was the best money. Likewise, finding lodging outside London and commuting by train is a viable alternative to the high cost of London hotels. You'll likely find that all of your lodging (outside London) will be less than a single night in London. Don't forget about Bed & Breakfast offerings.
Lastly, get the addresses for the various guns shops(Purdey, H&H, Boss, Evans, Beretta, etc) and plot them on a London map as best you can. Then plan on using the London taxi services to get you from shop to shop. It will be time well spent. I can't count how many times I went to H&H, and was amazed each and every time I was there.
