Tens of thousands of SSE customers are being urged to go after the company for compensation after regulator Ofgem said it was fining it £10.5 million for "prolonged and extensive" mis-selling.

Chancellor George Osborne described the penalty – the largest ever imposed on a supplier – as "quite right" and said he would like to see the proceeds of future fines given to customers rather than the Government.

The company, formerly known as Scottish & Southern Energy, was punished for consistently misleading customers about its fees to encourage people to switch accounts. Customers were mis-sold gas or electricity.

SSE already has a £5m fund set aside to compensate affected customers from a previous mis-selling investigation.

But Ofgem has warned the numbers affected are likely to run into many more than the 23,000 they estimate were mis-sold on the doorstep and in-store. Thousands more are also expected to have fallen foul of mis-selling by telephone.

Ofgem said: "The authority also notes that given the serious contraventions that have occurred, the payment of compensation of this kind is no more than it would expect of any conscientious licensee.

"The authority does encourage all consumers who think they may have been exposed to mis-selling by SSE agents to consider applying - for redress."

The compensation fund has been in place since the end of 2011, when SSE was under investigation by Ofgem for misleading doorstep selling. It was found guilty and fined £1.25m by Ofgem in May 2012. So far £400,000 of the fund has been paid out to 6500 customers, an average of £61.50 each.

Management at SSE – one of Britain's "big six" energy suppliers – were accused of failing to pay enough attention to compliance, which allowed the mis-selling to take place.

Ofgem said customers contacted by SSE were exposed to misleading statements, in-accurate and misleading information on SSE's charges, and misleading comparisons between SSE's charges and costs of other suppliers.

Some customers were told they would save money by switching to SSE, only to find their bills went up as a result. In one case cited by Ofgem, a woman who was promised a £177 saving if she signed up with the utility actually saw her bills increase by £134 a year.

In an example from one doorstep script used in the north of England, the salesman was recorded as saying: "What I'm here to do today is show you a Government thing called de-regulation, which results in your energy prices being lowered by doing nothing at all."

The statement was inaccurate and misleading as there was no automatic reduction in energy prices resulting from "a Government thing called deregulation" or from the customer "doing nothing at all", said Ofgem.

Ofgem's investigation into mis-selling in the energy market has already led to it agreeing a £4.5m settlement with EDF.

The regulator, which began its investigation in October 2010, is still looking into suppliers ScottishPower, npower and E.ON – which was the latest to learn of a probe into its sales techniques in April last year.

Ian Marlee, managing director for markets at Ofgem, said: "This [£10.5m] fine represents the fact that what they were doing was allowing a culture of mis-selling to continue, they weren't doing enough to prevent sharp selling practices from their selling agents, they actually provided misleading sales scripts."

Mr Osborne added: "SSE have treated their customers badly and it's quite right they've got this big fine."