Do you want a debit card or a credit card? - Natwest do a Step Account that gives you a debit card and DD facility, but no overdraft. For credit Cards, go to Capital one or Vanquis. The two credit card companies are an absolute rip off though - only get one if you are sure that you are able to pay the balance every month as the rates are really high - also look out for the fact that they try and get you to make late payments - theey nevare make it easy to pay.
Hope this helps.