I moved into my boyfriend's apartment earlier this year with every intention that we would move at the end of the lease term. However, as the term was ending he was in the process of looking for a job and asked our landlord whether we could rent month to month until he found a job and knew more about where we would be relocating. Our landlord agreed at first but then later told us we could only do month to month for 1 or 2 additional months. While we were looking for apartments, our landlord emailed us saying that if we agreed to stay, he would replace our crappy vanity and finish off a room in the back of the apartment that we had previously not been allowed to use. We agreed. About a month later, he did replace the vanity, which is nice, but he did a shoddy, incomplete job putting it in. He has not yet finished off the extra room OR given us a new lease to sign. Our contract clearly states that a new lease needs to be signed at the end of every term in order to renew. My boyfriend just got a job at the other end of the state and we decided that we really need to move. When we contacted him to give him 30 days notice, he sent back the email that my boyfriend had sent agreeing to the terms he had suggested to get us to stay and is now saying that we may be responsible for any interim rent after we leave and that we owe him $500 for the vanity. Does my boyfriend's email expressing our intention to sign a new lease negate the fact that we DID NOT actually sign one?

WHat state and country was this in... laws vary and certain localities MIGHT accept such an emaill as a binding agreement. We can't however assume it is without knowing that info, and maybe even what the email had specifically.