Re: What's a sailor to do in London?
Haven't been to the UK for a number of years, but getting around by rail on the weekends used to be problematic because that's when they did their railway maintenance. Be prepared with "plan B".
A trip to Portsmouth ("The Flagship of Maritime England") and neighboring Southsea would be worth your while. A walk from the port entrance (starting with a pint at the pub there) to the fort built by Henry VIII in Southsea will give you a better idea of the history of this historic, sea-based area, including harbor defenses across several centuries. The HMS Victory is a must see and you might also fit in a ferry ride to Ryde on the Isle of Wight to get the waterside perspective.