For me the confusion arrises when Eddie says "there is no VAT on the prices on my website" There is of course VAT included 'in' the web site price.
You pay Eddie £380, he pays £63.33 of that to the vat man. Obviously he is able to claim back any vat paid on his purchases.
The price of the watch for a UK/EU resident is £316.67 plus vat = £380
The price of the watch for a non UK/EU resident is £380 which includes no vat.
A generous way for Eddie to move from being non vat registered to vat registered but a little confusing.