Customers would need to make a choice, but some campaigners want those with low energy use to automatically move on to a deal free of standing charges.
“The problem with presenting a choice of price caps is many vulnerable people won’t make that choice,” said Martin Lewis, founder of Money Saving Expert.
One of those who could benefit would be Joanne Wilkinson.
“I try not to look [at the standing charges] because it’s depressing,” she said.
She said she had enough to worry about dealing with baby daughter Adeline, but noticed how quickly the meter goes through the money that was loaded on to it.
Lower wages in the north of England made it even harder for parents like her to afford energy bills, she said, especially as she was still on maternity leave.
But Energy UK, which represents suppliers, said that such a fundamental proposed change needed careful consideration.
“It would be a major undertaking to make all customers aware of this change and to ensure they then choose the best option for their circumstances,” said the trade body’s chief executive, Dhara Vyas.
She told the BBC the addition of a zero standing charge price cap option would “quite significantly change the nature of the price cap”.
“It would go from being one single regulated price that gives customers protection whether or not they switch, to a situation where I think customers might be expected to make an active choice about which cap they are on.”
Asked whether standing charges should be scrapped altogether, Tim Jarvis, director general of markets at Ofgem, told the BBC the option had been looked at, but added the costs “need to appear in bills somewhere”.
He said moving costs into unit rates could have “some quite bad effects on people in some of the most vulnerable situations”.
The regulator’s proposals do not deal with the variation of standing charges in different parts of the UK, with billpayers in some areas paying considerably more. Ofgem intends to make that part of a wider, separate inquiry.