Now accounts are paid for, from your card, by a Continuous Payment Authority.
If you ask your card issuer to stop one of these, then they can, and they must, and any further payments that they allow on the CPA, they must refund you for.
There is no need for you to stop the card being used, and indeed, this is usually ineffective, as CPAs are designed to cope with card changes - so you must stop the CPA, not the card.
Though if you think your card security has been breached such that payments other than CPAs can be fraudulently taken from it, then you do need to stop the card; but you still need, separately, to stop the CPA.
Have another word with your card issuer (which may or may not be your bank, though if you asked your bank to stop the payments, they should have told you that they were not the card issuer, if that was the case), quoting:-
Set a Payment PIN on your account so that no-one but you can buy memberships on it. Check your bank accounts monthly for any other unexpected payments to Now. That way you can at least nip them in the bud, while you and Now figure out whose fault they are.