However, Ofgem said on Wednesday that it would have to wait for legislation to be in force before it could take action on standard variable tariffs.
They argue intervention in the market does not promote competition.
Ministers confirmed that energy regulator Ofgem would be compelled to implement the cap once the law had given it new powers.
The UK's "Big Six" energy suppliers may suffer a knock to earnings by new legislation that puts a cap on energy and gas bills.
Under the bill, energy regulator Ofgem will be required to consult and impose an absolute price cap on standard variable tariffs (SVTs), which are default tariffs that can cost hundreds of pounds more than cheaper deals.
The prime minister said that the draft bill was a vital step towards fixing the "broken energy market" and "offering crucial peace..."
Ofgem had already proposed intervening in the part of the market that supplies more vulnerable customers.
The cap will apply to about 18mln accounts that use standard variable tariffs at least until 2020, and possibly be extended to 2023 if deemed necessary, under draft legislation to be laid out by the government later today.
Four million of those are on pre-payment meters.
The Government says it welcomes Ofgem's move, but claims the regulator could go further to protect everyone on default tariffs from the unfair practices affecting two-thirds of households in Britain.
Peter Earl, head of energy at Comparethemarket, said a price cap would not fix the broken market.
The bill will be published about mid-morning on Thursday, with the business secretary, Greg Clark, due to to make a statement in the House of Commons. While five million households will see their bills capped from this winter, I want to see every household protected from rip-off bills.
However, the ceiling on energy and gas bills is not expected to take effect until the winter of 2018/19 at the earliest.
The paper conclude that despite this, the largest players' ratings may not be immediately altered following the introduction of a tariff cap.
There has also been a guarded welcome for the draft Bill from consumer organisation Which.
"However, the Government must guard against any unintended consequences that undermine customer service and push up prices as a whole". Around 18m customers are now on SVTs or other default tariffs.