'Posh' places, like Fortnum & Mason, Brown's and the Dorchester, generally charge �25 to �40, so you'll have to come slightly 'down market':
The excellent Porter's Restaurant doesn't serve 'high tea', per se , but you could make some appropriate selections from their menu: http://www.porters.uk.com/
Yauatcha in Soho W1 is a Japenese Tea House with the most wonderful cakes and tea in the daytime and about �20 or less a head. In the evening it is a marvellous dim sum restaurant. If you fancy something a bit different try that!
Liberty's also do a nice high tea with champagne in their cafe. I think this is also less than �20.00. Hope this helps!
Sorry I thought High Tea and afternoon tea was a similar thing - I wouldn't say Porter's was a suitable suggestion for tea. In fact my husband had a unforgetable birthday there 3 years ago and wouldn't go back.