I've got a Scottish friend in Italy (but with a flat in the UK) with a very similar problem, which she asked me to look into for her. Unfortunately, as far as I could see, there's no way around it..
The two main areas of difficulty seem to be
(a) UK anti-money laundering legislation (which imposes restrictions upon who lenders can offer accounts to) ; and
(b) the natural reluctance of banks to lend money to people when they know that they'd have great difficulties pursuing through the courts if they were to default on their loans.
As Ubasses effectively indicates, BA and Iberia are actually part of the same company (IAG, along with Aer Lingus), so Iberia's card might be worth looking into.
(Iberia also sells Avios through Groupon:
https://www.groupon.es/deals/ga-avios-group-espana )