There are plenty of ATM's in Benidorm all of which accept Nat West cards.
Be carefull though and only use one's that are attached to the bank as opposed to the free standing one's outside shops. That way if you do have problems then the bank staff will be able to help you.
Also if the machine looks in any way that it has been tampered with don't use it. Just as you would in the UK.
You will get charged for using your card so find out how much before you go as if you use it often this could add up to quite a lot of charges.