Mark, there is one lighthouse right in London. It's at Trinity Buoy Wharf in the Docklands. It seems to be some sort of art center now.
Here's a couple of sites:
http://www.greenwichmarket.net/keely/TBW_homepage.htm http://www.pixcentrix.co.uk/sands/preview.htm This site's pretty neat. Doesn't have photos of all the lights but at least mentions some that don't get mentioned elsewhere. Check the Lighthouse Guide section for another mention of the lighthouse in the Docklands which is also called Blackwalls. There are some other minor lights in the River Section but they may be a way out of town???
There is also a former lightship in the Docklands which is now a restaurant, Lightship Ten.
http://www.lightshipten.com/main.html The train system in Britain is great if you want to take a day trip to the coast you have lots of choices. It's been over 10 years since I was there but at that time if you left after the morning rush and traveled 2nd class, which was fine, the prices were very reasonable. Ask for a return ticket which is British for round trip. The only coastal trip we took was to Dover. There are lighthouses there but I wasn't into them then so didn't look for them. But if you were to go there you can tour Dover Castle which has the remains of a
very old lighthouse!
http://europeforvisitors.com/europe/articles/dover_castle.htm The castle admission also included a tour of the secret WWII tunnels which was very interesting. The evacuation of Dunkirk was coordinated there.
In Dover you can also see the ferries and of course the white cliffs.
The South Foreland Lighthouse appears to be quite near Dover also.
http://www.britainexpress.com/countryside/coast/south-foreland.htm http://www.lanternroom.com/lighthouses/england/eng48.htm http://www.lanternroom.com/lighthouses/england/eng49.htm When we went to Dover there was a tourist info place right in town as we walked there from the train station.
Well we did also do a day trip to Wales but didn't go to see lighthouses although we were on the coast. You can easily do the south coast of Wales in a day too if you don't mind returning after dark. Or you can just go to Cardiff. I think there are lighthouses there. We went in March. And we also did Oxford which was wonderful. The college buildings and grounds are amazingly beautiful. I'm sure Cambridge is also but we didn't get there.
Get in touch with the BTA (British Travel Authority) and ask for all their materials. They have good city and country maps and can send you a rail map which is helpful. The tube system is very easy to negotiate. Buy a pass right at the airport. It seems we needed an extra passport photo for that.