If a tenant wants to end and agreement early they are required to give as much notice as possible, preferably in writing (keep a copy of the letter) stating the exact date they intend to leave.
You can claim compensation for any loss suffered as a result of the tenant ending the agreement early i.e. rent until new tenants move in or the existing agreement ends (whichever happens first), a reletting fee (usually one weeks rent when using an agent whom charges this fee onto you) and advertising costs.
However you cannot claim these expenses if the agreement was to end shortly as you would have incurred these costs anyway and you must make considerable effort to keep these expenses to a minimum by making the effort to find new tenants.