My suggestions for the slightly-off-the-mainstream would be:

1. Dine at http://www.supperclub.com/html/london/




2. Have a drink and party at the Shunt Rooms hidden behind an unassuming wooden door in London Bridge Station:

http://thewordofward.co.uk/?p=729





3. Climb the Dome of St. Paul's for some of the best views of the capital, and the incredible Whispering Gallery:

http://www.stpauls.co.uk/Cathedral-H...Climb-the-Dome

...where you can have a conversation with the person the other side of the gallery as if they were right next to you.




Oh, Shunt has closed. That's a shame.

well, this calls for a replacement, so in its stead, je propose:

3. Street skating around london http://www.lfns.co.uk/

London Friday Night Skate (LFNS) and Sunday Stroll are weekly marshalled street skates in central London. The LFNS departs from Wellington Arch at Hyde Park Corner every Friday at 8pm.

The Sunday Stroll departs from Serpentine Road in Hyde Park every Sunday at 2pm. Both are weather dependant and we announce if a skate is running a few hours before the scheduled start. The events are open to all skaters able to stop, turn and control their speed on hills.

The Sunday Stroll is a relaxed slow paced skate; the LFNS is faster, more technically demanding and may involve hills and sprints. We welcome both inline ('rollerblade') and quad ('roller skate') skaters. Children are welcome provided they're accompanied by a responsible adult willing to take them home if necessary.

Route information is usually published mid-week and can be accessed via the links above. You can also find us on Facebook, on Twitter, or subscribe to our weekly email newsletter. LFNS runs purely for the joy of skating. Participation is entirely free and the skates are staffed entirely by volunteers.

I was going to suggest pop up cinema:

www.popupscreens.co.uk/

Or you could try and get a ticket to look around one of London's closed tube stations:

http://www.bbc.co.uk/news/magazine-25576814

Sleeping on the tracks is not recommended...



Or you could google one of Lady Marmalade's parties.....