if you go during the week, then Claridges is the place to go. Saturday-Sunday is booked up 3 months ahead, unless you stay there for the night, which wouldn't be so bad
I've been staying at Mandarin Orientals around the world and always had amazing afternoon teas. Never had one at their London hotel though, so can't vouch for that. However, the MO bar is a perfect place to have a drink after a "shop-til-you-drop" at Harvey Nichols.