More than 11m households will have their energy bills cut by about £75 a year under a price cap being imposed by the industry regulator, Ofgem, following a political outcry over companies taking advantage of loyal customers.

The average saving falls short of the £100 that Theresa May promised for consumers on poor value default tariffs before she handed over responsibility for setting the cap to Ofgem. The overall saving from capping bills at £1,136 a year is expected to be about £1bn, which would largely wipe out combined profits of £924m made by the big six energy companies last year.

There are 11m UK households on the default tariffs covered by the cap, but only 3m of those will save more than £100 because they are either on the market’s most expensive default tariff or are high energy users. By contrast, those on the cheapest default tariff offered by the six large suppliers will save just £60.

The upper limit for default tariffs, known as standard variable tariffs (SVT), will be set at £1,136, based on typical fuel consumption and paying by direct debit, Ofgem said. The figure is in line with analysts’ expectations.

The average big six SVT is £1,220, though if npower or SSE announce a second price hike this year before the cap, like their rivals, that figure would rise. Ofgem could account for that in the final version of the cap, which is not due to be confirmed until the end of October.

Dermot Nolan, the regulator’s chief executive, said: “Ofgem has made full use of the powers parliament has given us to propose a tough price cap which will give a fairer deal to consumers on poor-value default tariffs.”

Greg Clark, the business secretary, said: “This government is delivering on its promise to end that injustice and protect households across the country from unjustified price rises.”

Labour’s Rebecca Long-Bailey, the shadow business secretary, said that while the price cap was a start, it was less than had been promised.

“Theresa May promised 17m households would be better off by up to £100. Today’s announcement is a smaller saving for fewer people. Despite promises from the prime minister, the government has continued to sit on their hands while the big six have hiked prices.

“Tory dithering means that millions of customers will now be even worse off than when Theresa May first made her promise.”

The share price of Centrica, owner of Britain’s biggest energy provider, British Gas, rose 5% on the news. Analysts at Jefferies bank said the cap was £12 higher than their estimate and the impact on Centrica would be manageable.

However, the industry body Energy UK said the cap would pose a “significant challenge” for some suppliers.

Nolan said some companies would have to become more efficient, a phrase which usually refers to job losses. E.ON has already announced 500 job cuts, which it blamed on the cap, and the merger of npower and SSE is expected to lead to further losses.

“We expect there to be lower profitability going forward. If they want profitability they need to make those kinds of cuts,” Nolan said.

The level of the cap will be adjustable every six months and it will be reviewed in April and October of each year. Changes will depend on costs facing suppliers, such as the wholesale price of gas and electricity, which has been rising this year. Bernstein bank said it could jump by £108 next April.

Nolan and industry watchers stressed that the biggest savings for households would still come from switching suppliers.

Comparison sites, which stand to suffer if switching falls because people think they are now protected, said the cap would still leave people overpaying.

uSwitch accused Ofgem of playing a “dangerous game” by presenting the cap as a fair price, given the cheapest deals on the market were about £300 lower.

“Don’t get lulled into a false sense of security by the political soundbites,” said Stephen Murray, an energy expert at Moneysupermarket.

The consumer groups Citizen’s Advice and Which? welcomed the cap as a step in the right direction but echoed the calls for people to shop around and switch.

It remains to be seen whether the big suppliers will all bunch their prices together just below the cap when it takes effect at the end of the year.

Under an existing, narrower cap for 4m vulnerable households on prepayment meters, all six have priced their tariffs at the same, maximum level allowed.