Hi Clairebrum, I suggest you try the Halifax Easycash account first. That gives you direct debits and a visa electron card so you can spend money electoncally. They have a nice online service and savings accounts you can use. Use it for a while and get yourself on the electoral register. After say after 6 months go in store and ask them for a full current account with a Visa debit card.
I know how annoying it is. My parents are on a state pension and keep being offered credit cards with 2-3k limits. But someone working and earning from abroad cant get nothing!