if you shop in london, most of the shop can do the tax refund immediately, just bring your passport and fill in the form, when you arrive at the airport, just go to VAT refund with those forms, they will give you back the cash or credit back to you card. Big store like Harrods, Selfridges, John Lewis will give back in cash, small boutique will refund back to your credit card.
pls note the vat is now 15% but they will charge 2-2.5% for the VAT deduction service charge, so not totally get all 15% back.
i suggest you to buy LV in London Selfridges, after shopping go to basement they have a VAT refund counter, you will see loads of tourist queue up to do tax refund, they will show you how much you can get immediately (after service charge), the counter just next to the Vera Wang wedding boutique