where is a good afordable place for tea in london?

Caffe Concerto on Picadilly might be suitable. Good quality, not too expensive, and not too formal. You're unlikely to stand out if on your own. The place itself is more modern than traditional. Many locations in London.

http://www.caffeconcerto.co.uk

Afternoon Tea for one is £16.

If you want something a little more unusual, try RIBA - Royal Institute of British Architects at 66 Portman Place just north of Oxford Circus. They serve tea from 2 to 3.30 pm. It's a gorgeous building and there are sometimes free exhibitions on there too.

Most of the museums have cafes and try the Crypt at St Martins in the Fields church in Trafalgar Square.

Continuing Jennifer's thinking... The British Museum does afternoon tea under the spectacular central glass roof.

We have had tea at several hotels and Harrod's and spent too much for what is offered. For our trip to London in September I have narrowed our choice to The Wallace Collection or Inn The Park (St James). The menus look affordable as well as tempting. You could check out tea at the Wolsley but our lunch there was pricey. Many rave about tea at the Orangery but it is not served like a proper tea and is a bit noisy.

Bea's Of Bloomsbury.

You can spend a lot or a little (for London). Brown's is high end and fashionable. Bea's is great and The Crusting Pipe is unique. http://www.afternoontea.co.uk/uk/london/covent-garden/crusting-pipe/

The choice is based on your interest and your pocketbook.

How about tea on a double decker vintage bus? I haven't done this, but it's on my list for the next visit and you might find it interesting; cost is pretty much the same as Harrod's but follows an interesting route.

www.bbbakery.co.uk/afternoon-tea/afternoon-tea-bus-tour

Brown's Restaurant in Covent Garden is very reasonably priced for their afternoon tea and it has a nice atmosphere. We also love the food here for lunch or dinner.
I also like the tea at Hush Brasserie - they have a location by St Paul's and Holborn...modern style with very good afternoon tea that won't break the bank.

I second Emma's suggestion for watching Groupon. There seem to be afternoon tea offers on there every day. We booked one for our upcoming visit. It is easy to sign-up to receive the e-mails from anywhere.

Agree with Groupon suggestion, and have bought Afternoon Tea from there before and it was very good, but, read the small print carefully. They are often very restricted as when you can use the offer, and you have to book it in advance. I've had Groupon's before where the time I wanted was unavailable.

I've also had a hotel lie about not having any places for popular times, as they will hope that you pick a less popular time, so they can maximise bookings. Can't blame the 5 star hotels for trying to screw the little guy though, they are barely scraping by as we all know (tongue+cheek).

Afternoon tea at The Orangery at Kensington Palace is wonderful.

Pam, we went on the afternoontea.co.uk website listed above and booked the St Pancras Grand and Champagne Bar tea. My confirmation email doesn't show the price (and it was in January, so I don't remember) but I'm confident it was less than 20 pounds/pp (the current price is 16.50/pp with the 25% discount). We didn't do the champagne tea, just traditional. I thought the restaurant was very nice and the service was good. The tea and food wasn't too shabby either... :D It was 2pm on a Saturday afternoon and it wasn't too busy! Oh, and we were dressed casually as well. We both wore jeans but we wore nice tops. Oh, and when we went last April, we went to St Pauls for tea. We were paranoid about being underdressed, and then the British couple next to us came in in logo t-shirts, Converse and jeans. So we felt fine when we saw that! I'm jealous. My husband won't admit it, but he loved afternoon tea!

Pam, by yourself in London or just for tea on a particular day, how wonderful. Browns Hotel is pretty high end, Browns restaurant is not. Love them both. Also the Orangery while being, I agree, a bit noisy, there was nothing improper about their service, plus you can see what's happening at Kensington Palace. Another of my favorites is Liberty, also The National Gallery.

There are many places that have wonderful afternoon tea, some very expensive. The Orangery services a very proper afternoon tea, very affordable.

Don't know the price, but check out the architecture on the Royal Opera House afternoon tea webpage. Hamlyn Hall looks like a grand place for tea!