I've heard that there is a way from London to Greenwich on a boat. The boat passes under the London Bridge.
So it is also good for London sightseeing with a reasonable price.
The starting point is a London Eye Pier which is just below the London Eye. While some companies seem to operate, but the Clipper is the fastest. I got on the Clipper by chance.
You can find out timetables and prices in the above site. I paid 12 pounds round-trip Ticket. It seems it was a little cheaper by using Oyster Card. So sorry I had it at that time. But it is not a big amount.
40 minutes from London Eye Pier to Greenwich. It was faster than I had expected. London seen from the river was also good.