While chargeback laws are a bit more restrictive in some EU countries, you should always have the option to ask your bank to block future charges, without changing your card.
A couple of years ago i found out netflix account was stolen, email address changed but card continued to be associated with the account. I couldn't login. Called Amex explained the situation and asked to block future payments. They refused on the basis that I agreed (originally) for netflix to take the subscription fee monthly so I had to contact netflix to solve to do this. Amex. The age where consumers have power over who takes money from them is gone