Hi,
There are many places that offer this service, at a variety of prices - The Ritz is the most famous, but also the most expensive and overbooked. I also think it trails behind several of the others - so would rather recommend others:
For award winning - try Brown's hotel or the Dorchester - expensive, but for good reason - the service is also impeccable. For a different twist - St. Martin's Lane hotel - offer 'Eastern' influenced varieties on the Afternoon Tea standard, which are tasty and imaginative.
Sketch parlour specialises in fancy pastries and is superb. The restaurant (Michelin starred) is very difficult to get into - but the parlour, is much less so.
For a very reasonable priced offering - try the Orangery in Kensington Palace - 1/3 of the price, and in suitably grand surroundings.
For more afternoon tea information - check the 'Afternoon Tea' section on the site I edit: #mce_temp_url#
Patrick