Shops should not ever mark something as a gift because they can be prosecuted.
It's really hit and miss (and almost entirely depends on how they ship it, how big it is, what sort of packet it comes in, etc).
I run an online needlework shop, have all my stock sent through regular mail and only occasionally get hit for VAT.
VAT in itself is not really the issue. It's usually only a couple of quid. The stinger is the "handling fee" charged by ParcelForce, and more recently, the Royal Mail. I've had parcels come where the total customs charge was £2, but had to pay £12 "handling" because I had the audacity to order it in December.
In my experience, if it is sent USPS Global priority, you WILL BE CHARGED VAT and a handling fee by the UK postal service.
If it's sent in a plain envelope, or by an international courier, you won't (usually).
And I've never had a problem using a UK credit card on a US website.