There's a difference between afternoon tea and high tea - I'm guessing you want afternoon tea, which is tea, scones, finger sandwiches, pastries. High tea in England is just what they call a light supper.
For afternoon tea (3-5:30 most places) try the Orangery at Kensington Palace - it's one of the cheapest I've found. £12 for afternoon tea - they also have fancier ones w/ champagne, etc. for £18+. It's still fairly pricey considering the exchange rate, but it's a lot better than the £30-40 you'll pay at most hotels. No reservations needed. http://www.digbytrout.co.uk/branches/kensington/index.htm
Also look into tea at The Wolseley on Piccadilly near The Ritz - cream tea (tea, scones, clotted cream, jam) from £9.50 and afternoon tea for £19.50. Reservations are not necessary, but recommended. If you go to any of the fancier hotels, you'll want to make reservations several days in advance. http://www.thewolseley.com/