Nia
It depends on the particular card so go online and check yours out. If necessary telephone Customer Services.
Usually you should have no problems but it would be wise to just inform your card supplier before you travel that you will be using it in Greece just in case there is an automatic security block on any unusual transactions.
Some such as Nationwide specifically state on their web-site that you do NOT need to notify them for 2 of their cards but they also give general advice that you should always consider taking more than one method of payment when you travel abroad, e.g. debit card, credit card, cash and travellers' cheques.
We always take a few hundred euros in cash as well.
Dennis