My own supplier is Postcard Teas in Dering Street, just by Bond Street. They periodically have events there where a tea enthusiast, scholar or craftsman will make an informal cup of matcha. The range of matcha on sale is limited but the vendor has personal relationships with the growers, you won't find any dud examples (and there is no way you would ever be sold stale matcha).

Another place you might unexpectedly be offered a cup of beautifully prepared matcha is at the British Museum. There is a tea house there and occasionally there is a demonstration.

There's a chado (tea ceremony) society in Cambridge and they sometimes come to London to take part in events. http://www.kaetsu.co.uk/regeve.htm


I'll focus now on somewhere you can just turn up and buy a cup to drink:
There's a lovely wagashi (the dainty sweets that often accompany matcha tea) shop called Minamoto Kitchoan in Piccadilly. http://www.kitchoan.com/?page_id=7#lct-lo
It's open until 7pm and they serve matcha until 6:30pm.

If you do like it and decide you want to prepare it yourself at home, there are starter kits at the Japan Centre in Piccadilly and youtube tutorials, or you might like to have a chat with someone at Postcard Teas to discuss your options and the techniques you can try. The Japan Centre does offer matcha, but check the expiry date carefully. I strongly recommend buying matcha in small quantities, it is really unpleasant when it goes off and it goes off pretty quickly (hence the tip about storing in the freezer). I've had a couple of matcha flavoured sweets and cakes from the Japan Centre that had that horrible "wet hay" aroma that stale matcha gives off.

If you're looking for a milky matcha drink, there's Tombo which is a small restaurant/cafe close to South Kensington Station. They have fantastic cakes from Lanka (which does Japanese French style patisserie ever so well) and delicious matcha latte (or matcha milk).