Hello, I am solicitor with 20 years experience. I will try to answer this for you.
The short answer is no you don't. You would only have to pay if the flat was empty or leased to someone at a lower rent ( in which case you would only need to make up the difference between the 2 rents for 3 months).
Thank you. Can I quote a particular law at my landlord on this?
Are you still there?
I just want to be able to quote a specific act at him.
It seems my last answer didn't get sent to you so I will type it again.
This is general contract law. Under the original contract you had a duty to pay rent up until 15 March. However your landlord has a duty to mitigate his loss which he has done, through finding a new tenant. He can only demand rent from you if you leave and the flat is empty. If he is suffering no loss from your ending the contract early he is not entitled to any payments from you.
If he has relet the flat he has effectively agreed to the early surrender of your tenancy.