You'll find, unfortunately, that you have no grounds to refuse to pay rent. Something similar happened to me actually: I lived with a friend in rented accom - contract was in joint names. He decided 3 months into contract that he wanted to move out. He had to continue to pay rent or find a replacement tenant, otherwise he was liable to pay rent til the end of the term. It would be helpful to you if you could get your ex to find someone to take on your side of the tenancy, so that you dont become liable for rent. Might also be worth-while having a anon chat to landlord if possible.