For a small sum this is an expensive way to send money. I presume they won't take a card payment? Ask about a chq in euros (an International draft, cost around 10 quid).
Alternatively explain the cost involved & that it makes it very expensive for you, keep communicating & build a relationship, several friends have done this & had the need to make a deposit waived. It really is only to ensure they're covered if you don't turn up & many places will be willing to drop the idea with some reassurance.

When we paid the deposit of our hotel accomodation in corfu we used paypal. We were surprised that the hotel offered this facility to pay but it was so easy and free of charges

As Athensfan says, we have always managed to avoid paying a deposit. From speaking to Greek property owners they have more faith in Brits turning up (or letting them know if there is a change of plan) than Greeks

Thanks all but -

Afraid we are dealing with a Greek owner who is married to an English girl who insists on a deposit in Euros by bank transfer.

Anyone used Global Web Pay?

Its an expensive way to transfer a tiny amount of money.....try paypal that has already been suggested, or I'd book another studio apartment, we always book independantly and like other posters have said....we have never had to pay "up front" either.... offer them cash on arrival and see what happens?? or give them your credit card number to secure the booking?

Just to finish this off. I took the 25 quid hit on the deposit but paid the balance via Post Office free but only over 400 quid.

After events in resort this year we are looking for new accomadtion in Tolo for next year. Started while we were there to be honest