Your contract has terminated. Normally, the landlord would serve notice that the contract is ending and he wants the property back. If he hasn't done this and you want to stay, you should renew it. Otherwise there is a rolling contract in place. In this situation, either of you only need give one months notice, which may suit you both.
The tenant is not expected to give notice to move out at the end of the agreed Short Term Tenancy Agreement contracted term (unless of course the contract has a clause written in). You are expected to move out when the time is up unless you have a new agreement.
I would suggest talking to Shelter and going through the details of your contract and your situation with them - there may be clauses in your contract that make a generic answer invalid.
Edited 1 time(s). Last edit was 2018:11:30:11:18:17 by Angelina.