When I go to UK I usually rent a car from a company in Gatwick. They have oldish cars which have a fair few scratches and minor dents. The good news is they don't care if another minor scratch appears and they don't require a Credit Card.
When I flew into Heathrow I had great difficulty in renting a car without a Credit card, a debit card was not accepted (As of course, unlike a credit card, they could not claim for damage on a debit card).
I applied for a credit card from Nationwide whilst I as there. The problem was that it was cancelled shorty after issue as I did not live in UK. An email to their CEO got it reinstated.
So, it this case I would suggest you shop around at the cheaper end of the car hire market.
Good luck.
