The problem is when you pay by card. These companies use what is called a 'continuous payment authority', and you cannot stop them - only the company taking the money can cancel the arrangement. They even remain in force if you change card number, or if your card expires - there is an automatic system to update these CPAs.
Even if you were paying by direct debit, cancelling it can end up incurring further charges from a returned direct debit.
Cancelling a direct debit does not cancel a debt, it only prevents the company from taking the money... which is fine if you can prove that no debt is owed. Cancelling by phone, as many companies nowadays insist, there is no paper trail - insist on a letter or email from them acknowledging cancellation.