I'll try and answer all the questions raised via this one answer. First of all, I was not asked for any Visa verification apart from the usual 3 digit code on the back of the card. Secondly, the delivery address is the same as the account address. Thirdly, unless my address has been used fraudulently - as suggested - it is not blacklisted in any way. I have never had any bad debts, or have my bank cards been refused in any way.
I was going to ring Ebuyer this morning but they use a premium rate number for Customer Services, so I've sent them an 'Enote' instead. I'll report back here when I get an answer.
One final thing: this was my first order from them - and possibly my last - and they did ask me to email the requested extra security details to snipped-for-privacy@ebuyer.com - which is the address listed on their website, so it would appear to be genuine.