I did afternoon tea at Fortnum & Mason a few years ago and I just sort of watched what others did at other tables (without overtly gawking, of course).
I definitely ate more than a plateful of those teeny tiny pastries, but I was hungry! No one seemed to mind, and they offered to bring out more, so I guess that's okay.
Also, I believe you can order coffee, instead of tea, at most places, without a problem, as well. However, trust me when I say that I am also not a big tea drinker, but I still managed to drink a pot and a half of what it was I'd ordered because it was so good! We just don't know how to make tea here in the US, I suppose.
I'm assuming when you order, though, you'll still have to pay for two afternoon teas, but you'll probably only get the tea in one pot and two cups and saucers. That's how it seemed to work at F&M.