Ofgem has warned energy companies overcharging customers on their direct debits that they will be forced to repay the money.
The energy bill price cap increased by 54% on 1 April, adding £693 to the typical household bill.
However, a growing number of customers have since reported that their payments have increased by more than the energy price cap allows.
That means energy suppliers are, in effect, holding on to cash that should be in their customers' bank accounts.
Experts have warned that the problem is worsening the cost-of-living crisis for those already facing a significant financial squeeze.
"While a higher direct debit doesn't mean you pay for more energy than you use - as any overpayments are ultimately due to be repaid - it does mean far too much cash flowing from accounts now, which is often a nightmare amid the cost-of-living crisis," consumer champion Martin Lewis said.
On 3 May, the business, energy, and industrial strategy (BEIS) secretary Kwasi Kwarteng criticised suppliers for the practice.
"Some energy suppliers have been increasing direct debits beyond what is required," said Kwarteng on Twitter .
"Ofgem has today issued compliance reviews. Suppliers have three weeks to respond.
"The regulator will not hesitate to swiftly enforce compliance, including issuing substantial fines."
In parliament on Tuesday, Ofgem told MPs they were "alarmed" by stories of consumers being overcharged and that the regulator was taking steps to address the issue.
"The [companies] will be repaying that money back to customers, they'll need to rectify it," said Ofgem CEO Jonathan Brearley.
"But if you're in an enforcement case, you may argue that there's more - there's redress - over and above that.
"Now, whether to redress over and above that we try and do two things: one is if you can identify the group of customers who have been affected some of it goes back to them.
"But, secondly: we have a redress fund, which is targeted at vulnerable customers."
Following Ofgem's remarks, Kwarteng said: "Update - energy suppliers have met the deadline and responded to Ofgem's market compliance review.
"The regulator will now analyse their responses.
"I have been assured by Ofgem they will do this rapidly, and will take compliance and enforcement action where necessary."
Ofgem also warned MPs that the energy bill price cap could rise even higher in October and hit £2,800 - meaning energy bills will have more than doubled in 12 months.
On Thursday, Rishi Sunak announced a £15bn package of financial interventions to ease the squeeze on struggling households.
Among the measures was £400 off energy bills for every household, regardless of their household income, with more extensive support for those on lower incomes - such as benefit claimants, who will also receive a £650.
Read more: Cost of living: What is the energy price cap and why are bills rising so sharply?