You can claim VAT refund at the International Currency Exanage located in 339 Oxford Street, London. Or the one at Westfield Parade, Unit C 302A, Ariel Way, London. If you are near Edinburgh, you can go to Fexco Money Exchange located in 3 Princess Street, Edinburgh.

You will need to fill your credit card or debit card details for the refund. Anything over 1000 pounds can only be processed at airports.

If you have claimed VAT refund anywhere esle other than the airports, you still have to get your form checked and stamped by a customs officer at the airport.
Otherwise, you will be charged a penality at the rate of 1.5 times the tax you have claimed.

For information about tax free shopping, you can check here. If you want to know UK's regulation regarding who can claim VAT refund and how, you can check HM revenue & Custom's site.