Account still being debited

In July 2013 I cancelled my insurance and received a cancellation confirmation letter.To this day my account is still being debited.I phoned them earlier today (26 Feb 2015) and they confirmed that the policy was cancelled in July 2013 but imp**** that it was my responsibility to follow up with what I'm assuming is a different company that does the debits.I feel that it's unfair for them to expect me to do something that should be handled on their side.I have tried contacting them a few times after the initial conversation today but to no avail.