I am new here so firstly Hello, a trip to London is not any more expensive than any other major city in Europe, in fact I think London is cheaper than many other places, ok so if you want a hotel in the centre its going to cost, but the transport system is great so no need to be right in the centre.
I digress, Greenwich (Greenich) is the only place in London to visit if you are of a nautical bent, to get into the centre its either by mainline train or driverless Docklands Light railway, 1st stop is the Cutty Sark Tea Clipper, which I believe still holds the record for fastest sailing ship on the trade routes, it is amazing and now floats on a sea of glass so you can actually walk under the keel!
maritime museum/observatory etc as already mentioned, one other not mentioned is London's Cable Car across the Thames, only a few quid and an amazing few, but not as good as the Shard
Chartering maybe a problem with no RYA certification, and yes southcoast would be better in terms of more boats, but Solent Sailing can be a bit like driving down a Freeway (I am getting the hang of the lingo) in rush hour, although its a great feeling.
You might also consider jumping a train to chatham (45 Mins) to visit the Historic Dockyard Kent Visitor Attractions, places to visit, Museums, Warships, Ropery, Submarine[/url] its where HMS Victory was Built and is steeped in Naval History along with being the location for the British Navy's darkest Days (when the Cheeseheads.....sorry Dutch invaded).
Its also where I keep my boat.......I would be Happy to welcome a sailor from across the pond for a day out if you were interested, (subject to me being satisfied that you will not try and make me squeal like a pig, and you that I am not actually Jack the Ripper in disguise)
Hope you have a great time either way, if you are interested in a trip drop me a PM or email.
P.S a few videos sailing in the UK https://www.youtube.com/user/nautica.../videos?view=0