Senior ministers have poured scorn on the idea of freezing private sector rents for a year, less than 48 hours after the Guardian revealed Rachel Reeves was considering it.

Steve Reed, the housing secretary, and Matthew Pennycook, the housing minister, became the latest government figures to criticise the idea, which has since been ruled out by No 10.

The government’s split over the idea has fed speculation about Reeves’ job after reports over the weekend that Keir Starmer was intending to sack her after the local elections.

Keir Starmer failed to guarantee she would remain in place during Wednesday’s Prime Minister’s Questions, though Downing Street insists she retains the prime minister’s support.

Pennycook said on Wednesday about the rent freeze: “We are not doing this. It’s not a credible or serious policy proposition.”

He added: “I can’t remember how many times I’m on record of saying this government has no intention, does not agree with rent controls, and there are really good reasons for that.

“We exhaustively went through the evidence of countries like Sweden, Germany, cities like San Francisco. Look at the Scottish experience. Now look at what happens to rent increases outside of tenancies where you have that form of control.”

Some experts argue that rent controls bring down rents for regulated homes, but push up those that fall outside the policy, whether they are in the same area or nearby.

Pennycook’s comments came after Reed gave a similarly scathing response to the idea, saying: “I’ve been crystal clear – we’re not doing it.”

The immediate pushback to the idea has prompted renewed questions over the chancellor’s future in government.

Kemi Badenoch, the Conservative leader, asked the prime minister in the Commons on Wednesday: “This is not a serious way to run the economy … Will he listen to businesses, listen to the country, and reshuffle the chancellor?”

Starmer responded by praising Reeves, but did not explicitly guarantee she would not be replaced as he has done in the past.

Downing Street said afterwards: “[The prime minister has] full confidence in the chancellor.” Asked to repeat Starmer’s previous guarantee that she would remain in post until the next election, a spokesperson said: “That position remains unchanged.”

Reeves’ allies have dismissed reports over the weekend that the prime minister was intending to sack her as “one final roll of the dice” to stay in power after heavy local election losses. One described it as “bollocks”.

Reeves herself spent Wednesday morning speaking at an all-staff meeting in the Treasury, flanked by her ministerial team, thanking officials and urging them to press ahead with the government’s mission of kickstarting economic growth.

Treasury sources said she highlighted recent decisions, including cuts to utility bills in November’s budget; and repeated her insistence on avoiding a costly kneejerk response to the Iran crisis.

One ally insisted the chancellor’s tone was “massively upbeat” and forward-looking, promising more detail soon on AI policy and the UK’s relationship with the EU.

However, a source close to Reeves’s team suggested they had been spooked by recent reporting about divisions in No 10 over whether to hold an immediate reshuffle after next week’s local elections.

City investors are watching Labour’s internal ructions closely, with some warning the prospect of a leadership race could push up the yield, or interest rate, on government bonds, still further.

A research note from analysts at the investment bank Jefferies called next week’s polls “the local elections markets can’t ignore”.

Yields have already risen sharply since the outbreak of the Middle East war as investors fear higher inflation and rising interest rates, potentially wiping out much of Reeves’s “headroom” against her fiscal rules.

The government’s borrowing costs jumped afresh on Wednesday amid fears of a prolonged conflict, with 10-year yields at their highest closing level since 2008, well above 5%. Reeves’s allies believe the threat of gilt market chaos is a strong argument for keeping her in place.