Are there an inordinate amount of Americans in these comments?
Debit cards are by far the most common method of card payment in the UK, if not the EU (i'm not sure what the stats are on that).
I have had issues with my debit card before. However, my "bank" (actually Nationwide Building Society) has always been very, VERY prompt with card cancellation, refunds, etc. etc.. To the extent that it is sometimes annoying.
For example: I withdrew money from a cash machine that had been linked to crime. So my card was locked until I went through security (via phone) and confirmed certain transactions weren't fraudulent. This has happened quite a few times.
One time my card details were stolen somehow and people were buying PS3s in Denmark and were attempting to do so in bloody Vietnam too. I got the large sum (the PS3 costs) back almost immediately, and was able to get the unauthorised overdraft fees reversed at a local bank branch. I explained to them that my Credit Card payment (also with Nationwide) would be impacted and they understood this and were accommodating. The only thing that took a bit longer was that there had also been a number of very small purchases (£1.90, etc. etc.) which were a lot more niggly to refund, which took about a week.