Afternoon tea, suggestions please

My London-fu is failing me - can anyone suggest somewhere that will do afternoon tea that's within easy reach of the British Museum?

Preferably this should be somewhere that doesn't need days and days of notice as the plan is for next Tuesday (so not the Ritz or the Savoy).

A friend is coming from Germany and she suggested afternoon tea, and (like a fool) I thought she had somewhere in mind, but now she's emailed and she doesn't. She's asked me. But the only two places I can think of would be too expensive and probably a bit far from where we're meeting.