An investigation by watchdog Ofcom found that the ISP broke a fundamental billing rule by continuing to charge a group of customers for landline and broadband after they had cancelled services.

In total, customers were overcharged by more than £500,000.

Plusnet has apologised for the error.

Lindsey Fussell, Ofcom's consumer group director, said: "There can be no margin for error, and no excuses, when it comes to billing customers correctly.

"This fine should serve as a reminder to telecoms companies that they must adhere to Ofcom's billing rules at all times, or face the consequences."

A spokeswoman for the ISP said: "We are very sorry and would like to apologise to the 1,025 customers affected. We reported this ourselves to Ofcom and made every effort to contact these customers to arrange a full refund before the investigation started.

"We would also like to reassure all customers this was an isolated historic issue and we have implemented a number of new robust measures to make sure this doesn't happen again."

Plusnet has made repeated attempts to refund all affected ex-customers by letter and phone. It has refunded 356 people a total of £212,140, which included interest at a rate of 4% for each of them.

The remaining funds, for customers whom it could not contact, have been donated to various charities.

The fine, which will be passed on to the Treasury, must be paid within 20 working days.