The Piano Works
The Piano Works bills itself as 'London's only non-stop live music venue'. Its two pianists and accompanying musicians only play music requested by the audience, so you can eat, drink and dance to live renditions of your favourite songs. Each night of the week has its own theme (e.g. Tuesday has offers on cocktails).
The nearest Tubes are Chancery Lane (Central) and Barbican (Circle, Hammersmith & City, Metropolitan) but Farringdon (Thameslink) is slightly closer than either.