The Treasury has been forced to dampen speculation of an imminent announcement on the cost of living for a second successive day, after Boris Johnson hinted to Tory MPs that the government was poised to cut taxes.

MPs said the prime minister had gestured at the idea of tax cuts to help struggling households, including at a Downing Street garden party for backbenchers.

Chair of the Northern Research Group, Jake Berry, told Sky News the PM was “showing more than a bit of ankle” to colleagues on tax cuts.

A Treasury source played down the idea, however, suggesting that in his conversations with MPs, Johnson had simply been “echoing the chancellor’s ambition to cut taxes for people”, which Rishi Sunak had set out at his spring statement.

It followed Johnson’s suggestion in the House of Commons on Tuesday that he and Sunak would say more about the cost of living “in the coming days”, which led to speculation of an imminent Treasury statement.

One former minister said Johnson’s comments to colleagues had not seemed fully formed or coordinated with the Treasury, and said it added weight to the prospect that Sunak could be moved at a reshuffle in the summer.

It is understood the chancellor is privately examining options for measures that could be announced before the summer recess, when it has become clearer how much energy regulator Ofgem will allow bills to increase in October – though it is unclear whether these will be substantive enough to satisfy the PM.

Johnson will hold a cabinet meeting in Staffordshire on Thursday in an attempt to underline his government’s mission of levelling up the UK.

Asked about the cost of living on a visit to Finland on Wednesday, he said: “We will have the maximum energy, effort and ingenuity to help the British people. You know the money we’re already spending. Of course there will be more support in the months ahead, as things continue to be tough with the increase in energy prices.”

One person with knowledge of the Treasury’s thinking said: “The chance of doing something sooner rather than later is on the up.” They suggested a temporary VAT cut was unlikely, because it would push up inflation whenever it is reversed.

Instead, options could include directly compensating users for the increase in energy bills – particularly if the rise is not as severe as had been feared before recent falls in the wholesale gas price – or extending the council tax rebate many households received in April.

Meanwhile, cabinet ministers have been asked to come up with deregulatory measures that could cut costs for consumers without requiring Sunak to sign off on more spending, with the first of these likely to be announced within days.

Some MPs would like to see the income tax cut Sunak has promised for 2024 brought forward; but with 80% of the benefit going to the top half of earners, it would do little to alleviate poverty.

Calls from MPs from across the Tory party for the government to take a more generous approach have intensified since last week’s disappointing local election results.

“The pressure on Rishi is huge, at the moment,” said former work and pensions secretary Iain Duncan Smith, who has called for universal credit to be increased to help the lowest paid.

He said the Bank of England’s decision to raise interest rates last week meant the Treasury should loosen the purse strings to prevent the economy sliding into recession.

“You’ve got to keep growth going,” he said. “You have to loosen fiscal policy: the Treasury have got it completely wrong.”

Carlisle MP John Stevenson said he expected the government to do more, particularly for the poorest.

“Help has to be realistic, therefore targeted at the least well off,” he said. “Universal credit is possible, also another look at council tax or the taxes on energy are the sensible options.”

Wycombe MP Steve Baker called for policy changes, including tax cuts and deregulation, to kickstart growth.

“In the short run, I am always going to be worried about too many constituents not being able to eat, or heat their homes: that’s why I wanted to maintain the £20 universal credit uplift,” he said.

“But in the long run, it’s very clear that the welfare state is not going to meet longstanding spending pledges. That’s why the PM must go for growth.”

Michael Gove was criticised on Wednesday for putting on a series of accents, when asked about speculation of a split between Johnson and Sunak.

He said on TV: “It is an example of some commentators chasing their own tails and trying to take a statement that is common-sensical, turning it into a ‘major’ capital letters ‘big news story’.

“When the Treasury quite rightly say ‘calm down’, people instead of recognising that they have overinflated the story in the first place then say: ‘Oh, this is clearly a split.’”

Responding to Gove’s interview, in which at one point he appeared to be imitating a Liverpudlian character played by the comedian Harry Enfield, Angela Rayner, the deputy Labour leader, said: “Is the cost of living crisis just a joke to them? This is not a serious government.”