We've been living in our flat for over a year with no contract while the landlord has tried to decide whether or not he wants to get a new estate agent.

In the meantime, the rent payment still goes to the estate agent, but like I said, there's no contract. DH last signed one over 2 years ago, shortly before I arrived.
Well, we're planning to move soon, we hope. So, what kind of notice should we plan to give? And who do we give it to? We assume we should let the landlord know, not the estate agency - he's the one we've been talking to the last few months about repairs needed around here, like the new roof, etc., but how much notice? A month? Or should DH dig out his last contract and see what it says in there?
I tried to google to find out what the legal minimum might be, but came up with nothing...