Npower has eight call centres, including at Oldbury, where it employs hundreds of staff.
It also has call centres in Rainton, near Sunderland, which employs about 2,000 staff, Hull, Leeds, Birmingham, Solihull, Worcester and Swindon.
The news has been described as a "body blow" by unions, especially coming just weeks before Christmas.
Workers were given details at briefings on Friday, with the company saying it was facing an "unsustainable business situation" which has persisted for a number of years.
The job losses will take place over the next two years, mainly at call centres, but it has not yet been revealed at which sites.
Johannes Teyssen, chief executive of Npower's owner, E.ON, said: "The UK market is currently particularly challenging. We've emphasised repeatedly that we'll take all necessary action to return our business there to consistent profitability.
"For this purpose, we've put together proposals and already begun discussing them with British unions."
E.ON UK chief executive Michael Lewis said: "With Npower becoming part of the new E.ON – creating the second largest supplier in the UK – we need to build a sustainable business with a lower cost base that allows us to compete in this extremely challenging market.
"We are proposing a number of steps to create an E.ON business that can be both sustainable and successful for the future whilst also fully supporting and serving our customers today.
"For Npower and its employees, these proposals will mean significant changes. We're aware of the impact these proposals will have and there will be appropriate levels of employee support at this time.
"Npower will now consult and work with with trade unions and employee representatives on all these proposals and we are committed to mitigating impact on colleagues.
"The background to these decisions is of course the unprecedented upheaval in the energy market. In the last 18 months we have seen almost one third of suppliers going bust or continuing to operate at a loss.
"What we're announcing today is our response to this difficult situation in order to remain sustainable."
A GMB spokesman said: "Clearly this announcement will be a body blow to Npower workers across the UK.
"The Government has to urgently wake up to the impact that the price cap is having on good and reasonably well-paid jobs in UK energy companies.
"Npower is a poorly managed company with significant losses in the UK but it's always the workers that face the brunt of poor management coupled with regulation that sends work overseas whilst sacking energy workers in the UK."
E.ON said it was stepping up its "ambitious cost-cutting efforts" without losing sight of its customers, adding: "This is based on leaner, increasingly digital processes that also improve the customer experience."
Unison general secretary Dave Prentis said: "This is a cruel blow for Npower employees. They've been worried about their jobs for months. Now their worst fears have been realised, less than a month before Christmas.
"The UK energy market is in real danger of collapse. If nothing is done, there could soon be other casualties.
"Npower's demise means there's no time to waste. It makes the powerful case for bringing the retail arms of the Big Six energy firms into public ownership.
"This would preserve jobs, ensure customers get a better deal and allow the UK to meet its carbon neutral targets."