Hello
I've mainly enjoyed afternoon tea at the more renowned hotels where reservations for large numbers will be difficult to make.
Have you tried The Goring? They always appear so accommodating and aren't too stuffy/fussy unlike some of the old school stalwarts.
Otherwise, you may get lucky at the Mandarin Oriental. I can't say that the bar/restaurant they host it at has much character, but you may be able to swing a last minute reservation there.
Presumably, the venues listed in this article are all fully booked? -
http://www.telegraph.co.uk/travel/desti ... -teas.html
Good luck! I'm sure you'll be able to swing something!