Amazon will certainly send stuff to op locns, and refund VAT (provided you are in a locn where there is internet, natch). Order in the usual way, and when they send an email to say the goods have been despatched, click on help/ordering/payment options and VAT, and request a VAT refund. You will get an email back to say the VAT has been refunded.
The only problem I encountered, as did several others, was that Amazon use ParcelForce to deliver to Mill Hill. In some cases, the parcel doesn't arrive, and Amazon send an email stating that as the goods have been returned they've issued a refund. On investigation it looks as if ParcelForce are returning parcels they fail to deliver within the time limit.
Most firms I tried to get VAT free from either won't deliver to BFPO (too much hassle with BFPO contract/only use couriers), or will only do VAT forms for reclaim, but this only works for tourists collecting the refund at the airport.