if your bank is one of the mainstream banks (lloyds, Natwest, Barclays etc) you can go to one of their branches taking ID with you (driving licence etc) and they will allow you to draw cash out. Many Post offices also will do that on behalf of a number of major banks.
Edit - thinking about it, the post office may have a problem doing it if the chip cannot be read - so a bank branch is your best bet. Some banks also have an emergency cash facility for occasions where the card is lost or where the chip is not being read - they give you a code which you enter into a cash machine for a one off cash withdrawal.