Boris Johnson has warned energy companies that sky-high bills will damage their business, speaking at a round table with the electricity sector where the chancellor of the exchequer cautioned that “extraordinary profits” were being evaluated.

No new measures have been agreed to ease pressures on household bills and any specifics are likely to be delayed for weeks until a new prime minister is in place.

Nadhim Zahawi met the providers along with the prime minister and the business secretary, Kwasi Kwarteng, amid tensions in government over the future of further windfall taxation.

One industry source briefed on the talks said it was “clear the windfall tax is not a preferred option for anyone – ministers or electricity companies”.

The short-notice attendance of the prime minister at the scheduled meeting raised some eyebrows in Whitehall and one source hinted it was a PR exercise, adding that there was little the long-scheduled meeting could agree within the constitutional boundaries of a departing prime minister not making major fiscal decisions.

The government faced mounting criticism for not acting now from key figures including MoneySavingExpert’s Martin Lewis and the former prime minister Gordon Brown.

New analysis by the Tony Blair Institute (TBI) also laid bare how the help offered so far by the Tory leadership candidates was unlikely to make a dent in the rises.

Liz Truss’s plan to reverse the recent increase in national insurance contribution would save households on the lowest incomes an average of just 76p a month, it found. The same tax cut would leave the richest households in the UK better off by £93 a month.

In an article for the Times, her rival, Rishi Sunak said he was prepared to find up to £10bn to help households this winter, in a challenge to the foreign secretary to make further commitments.

But Sunak’s plan to cut VAT on fuel was also judged to have little potential impact by the TBI. For the typical household it would only amount to a saving of about £14 a month.

The TBI chief economist, Ian Mulheirn, said the proposals so far would do “almost nothing to help the people who are most exposed this winter”. He added: “A serious response will require the new prime minister to extend and expand chancellor Sunak’s support package. The cost will be in the tens of billions, but there is no alternative.”

At the meeting, Zahawi said energy companies had agreed to “do more to help the people who most need it”, but did not say what that would entail. No further explicit help is likely to come before a new prime minister is in place.

Those attending the meeting included Chris O’Shea, the chief executive of the British Gas owner, Centrica, Keith Anderson, the chief executive of Scottish Power, and Simone Rossi, the boss of EDF in the UK.

The Treasury said all the ministers stressed the need to find new ways to help vulnerable customers. The crunch talks came with new predictions that Ofgem could raise the price cap to £5,038 next April, according to the energy consultancy Auxilione.

Johnson, Zahawi and Kwarteng also urged the companies to use their bumper profits to invest more in North Sea oil and gas and in renewable energy sources such as biomass, with hints that the government was watching closely to see that the extra billions were being reinvested.

A Treasury spokesperson said energy bosses were told the market was “not always functioning for consumers, and extraordinarily high bills will ultimately damage energy companies”.

In a hint that ministers had not ruled out further taxation, Zahawi said the government “continues to evaluate the extraordinary profits seen in certain parts of the electricity generation sector and the appropriate and proportionate steps to take”.

But although Zahawi hinted overnight that an extension of the windfall tax could not be ruled out, Liz Truss, the frontrunner to be the next prime minister, has made it clear she is not in favour of further taxation, arguing it discourages investment. Kwarteng, a close ally of Truss and tipped to be her choice for chancellor, has also opposed windfall taxes.

In a statement after the meeting, Johnson said it would be “a difficult winter for people across the UK” and that the government “will keep urging the electricity sector to continue working on ways we can ease the cost of living pressures and to invest further and faster in British energy security”.

Officials are drawing up a list of alternatives for whoever becomes prime minister on 5 September. The Liberal Democrat leader, Ed Davey, a former energy secretary, said people could not wait for extra support until a new prime minister was in post.

“Whether it’s Johnson or Zahawi, Truss or Sunak, not one of them has a big enough plan to help millions of families cope with soaring energy bills. That is why the Liberal Democrats are calling on the government to cancel the energy price hike to avoid a country-wide catastrophe.”