Just over a year ago I let my house through a local estate agent. The agent found a tenant and charged a fee for this but has been involved since. They do not manage the property and since the tenant moved in they pay me directly.

I have just received a letter from the estate agent with a bill for 1 more year for this tenant.

Is this correct? I was under the impression they could only charge this if they were actively managing the property, i.e. collecting the rent, maintaining the property etc.

You signed a contract with the agency, so you will see what you have committed yourself to in that agreement.

If you want to get rid of the agency, you will either have to buy out the contract, or let the tenant go, and find your own tenant.