Around 18m customers are now on SVTs or other default tariffs.
"While we favour free markets, we will take action to fix them", May said.
The Government's proposed bill to provide price protection to those who remain on poor value default deals, such as the standard variable tariff, will give these households peace of mind about the price they pay for their energy.
The draft Bill follows Wednesday's announcement by the energy regulator that it is to extend its prepayment price cap to one million more vulnerable households this winter, saving them £120 a year, although it admitted this would not take effect until February.
The Bill putting a cap on tariffs is being published in draft and scrutinised by the Business, Energy and Industrial Strategy select committee of MPs, in a move the Government says will help build a cross-party consensus. This is created to build cross-party consensus on how the price cap will work.
Four million of those are on pre-payment meters.
The Government said it welcomed the action by Ofgem but believed this could go further to protect everyone on default tariffs "from the unfair practices now seen in the market affecting two-thirds of households in Great Britain".
Dermot Nolan, chief executive of Ofgem, said: Ofgem shares the Government's concern that the energy market is not working for all consumers and is determined to reduce the detriment suffered by those overpaying for their energy, particularly those who are vulnerable.
However John Penrose, a Tory MP and former minister, told The Telegraph: "A temporary relative price cap puts the customer in charge, so energy firms compete to offer the best, most creative and attractive deals. While five million households will see their bills capped from this winter, I want to see every household protected from rip off bills".
"A Labour government would immediately introduce an emergency price cap while we transition to a fairer system for bill payers".
The draft bill is expected to be published on Thursday.
Alex Neill, Which? managing director of home products and services, said: "For millions of consumers anxious about their energy bills, a cap might sound like a positive move". While the price cap will benefit apathetic customers that don't switch, it is also likely to push up fixed prices at the lower end of the market as suppliers look to recoup earnings from their most profitable SVT customers.