Ofgem has warned energy giant Npower to resolve its billing problems by the end of August or halt all telephone sales to new customers.
The regulator said Npower must meet monthly targets to cut the number of accounts affected by late billing from around 400,000 currently to 100,000 over the next three months or stop all proactive telesales activity.
Ofgem has also opened an investigation into Npower's "prolonged customer service failings", the first under its new Standards of Conduct which state that suppliers must treat consumers fairly.
It warned that Npower could face a financial penalty or redress payment if it is found to have broken rules.
Earlier this month Npower said it would no longer send bills to customers who left it more than six months ago if the company itself was to blame for the delay.
The move followed reports of households switching away from Npower only to receive bills months, and in some cases over a year, later, while some existing customers had also reported bills arriving late.
One former customer tweeted MoneySavingExpert.com saying they left Npower last June and only recently received a bill for more than £1,000, while another said they had received a £350 bill 16 months after they left.
Under Ofgem rules, a customer's old supplier has to make "all reasonable effort" to close the account within six weeks and should then send a final statement showing money owed.
Yesterday consumer group Which? reported that Npower received 83 complaints for every 1,000 customers in the first quarter of this year - the highest number among the"big six" companies - and up from 49 complaints per 1,000 at the same time last year.
Npower admitted in September that a computer glitch caused by a transfer to a new billing system had caused various problems with around 700,000 customer accounts.
In December, Npower chief executive Paul Massara wrote to all 3.4 million customers apologising for the problems and pledging that no-one would be left out of pocket as a result of billing failures.
The company also made a £1 million goodwill gesture to vulnerable customers.
Ofgem said there had been some progress since it agreed on a recovery plan with Npower in December, with the company tackling long-standing problems in relation to new customers and the set-up of direct debit payments and clearing many of the oldest cases of late billing.
But it said Npower had not progressed as far and fast as necessary.
Ofgem's senior partner in charge of enforcement, Sarah Harrison, said: "Npower customers have suffered service failures for too long. That's why Ofgem has secured binding commitments from Npower to reduce its bill backlog or face curbs on sales, alongside launching a wider investigation under Ofgem's new Standards of Conduct.
"Ofgem has been monitoring Npower's service closely and we have been increasingly concerned about the slow progress to tackle failings.
"Npower's recovery plan has not delivered as far and fast as is necessary. Our analysis of complaints data also raises some serious concerns which will be thoroughly examined in our investigation."
Npower repeated its apology to customers, saying it had assigned an extra 650 people since December and planned to invest £20 million this year "to fully resolve customer service issues".
It is currently billing 95% of newly joining customers and 92% of all customers on time.
Mr Massara said: "We are committed to getting things right for our customers but recognise that, despite the progress we have made, our current billing standards have fallen short of where everyone wants them to be.
"We are happy to provide the assurances agreed with Ofgem, with whom we share the same objective of getting our customer service to where it needs to be. We will co-operate with Ofgem on the investigation they have announced.
"We are confident that the measures we are already taking and the additional resource announced today will bring our customer service back to normal levels of performance by the end of August.
"If we have not met this late bill target by then, we will suspend all outbound telesales activity to new customers and not sell additional fuels to existing single fuel customers until we do.
"I want to reiterate again that our customers should not lose out financially as a direct result of our billing system problems and that, if customers are worried about a high bill, we'll work with them to reach a suitable payment plan."
Which? executive director Richard Lloyd said: "Npower are consistently the worst for consumer satisfaction and this week topped the list for customer complaints, so Ofgem is right to take tough action.
"It is completely unacceptable for energy companies to neglect the basics of customer service. If they are unable to look after their existing customers then clearly they have no right to new ones."
Energy Secretary Ed Davey said: "It is unacceptable that so many Npower customers have not received the customer service they deserve and I fully support Ofgem's intervention.
"Our reforms are making it easier and quicker for people to switch energy suppliers, particularly to the growing number of independent suppliers, so all energy companies need to be doing more for their customers."
Citizens Advice chief executive Gillian Guy said: "Exposing customers to bill shock is completely unacceptable and can throw household budgets into disarray. For people struggling to make ends meet, finding hundreds of pounds to pay a large bill out of the blue can be impossible.
"We welcome Ofgem's intention to tackle this with energy companies.
"Providing accurate bills and dealing with problems quickly are the basics of decent customer service for energy suppliers. Npower is a long way from providing that at the moment. Npower needs to put things right much more quickly and compensate customers for the problems caused.
"As part of Ofgem's investigation we will continue to provide the regulator with evidence from consumers about their experiences with Npower and all energy suppliers."
Shadow energy secretary Caroline Flint said: " This should be a clear lesson to the energy companies: if you can't treat your existing customers properly, you shouldn't expect to be allowed to market for new customers.
"If the energy companies really want to show they're changing their ways, they should back Labour's plans for a price freeze and reforms to the market and put an end to overcharging and bad customer service."