Not in London (wails!), but in Berlin — where they run a small number of special open-top tours through their underground train tunnels.
These two hour subway cabrio tours are notable for the carriage you ride in – totally open top, with no glass reflections or ceilings to get in the way. Unsurprisingly, you’ll be wearing a hard hat on the trip.
The tours take place in on Friday evenings so as to avoid disrupting the normal service between April and September. Some background info here.
Imagine a really long roller-coaster ride, without the upset stomach, and a million times more exciting. With hard hats. That’s the U-Bahn Cabrio Tour.
The headset based audio guides are only available in German, so that might be an issue, but if not, and you fancy the sort of trip that London Underground SHOULD be offering, then tickets are now on sale here.