We use our Tesco card and pay it up each month - the vouchers are useful for shopping.
Jeza, you will need to give them bank details, they need assurance as to how you will be paying, and there is always a credit rating check these days - your good bank reference is essential. However - since you don't owe money, you may find your credit rating is not so high (crazy, but if you don't borrow, they don't know your track record) - so your own bank branch is probably a good place to start, as others suggest, where they will know your reputation.