For the UK, you have to fill up a form and hand it in at the airport. The line is usually very long. If I remember correctly, you get cash back on the spot. You can read more here.

In Japan, tax is deducted on the spot at the retail store; which means no hassle and queue at airport. Just need to make sure you have your passport along.

Depends on the AD/boutique you are dealing with and which country, other bros here should be able to share their experience
I bought a Tag in Amsterdam and only did a pre-auth of the VAT.
They told me if I do a VAT refund at the airport and mail back the form within a week, they won't charge the VAT. They even affixed a stamp on the envelope, all I had do was drop it into a mail box in the airport

Why not pick it up from Heathrow?
They actually have a wide selection there (even if not all of it is displayed).

Just picked a 114060 there and the best part is, you'd get quite a fair bit of points in Heathrow Rewards for future use.