Louise Haigh has urged Keir Starmer to avoid a “simplistic and naive” response by lurching to the right after Reform UK’s success in the local elections, in her first interview since being in effect sacked as transport secretary.

The former cabinet minister warned the prime minister to “pick some battles” with the right as it would not be enough to ask progressive-minded voters to back Labour at the next election just to keep Nigel Farage out of power.

Haigh was one of Starmer’s most prominent cabinet ministers on the “soft left” of the party and drove through his rail nationalisation bill, before she resigned as transport secretary in November when it emerged she had been convicted of fraud over a missing work phone a decade ago.

In her first intervention criticising the direction of the party, Haigh said one of the problems was that Labour was “shying away from the battles that we need to have” which would demonstrate to voters that the government was on their side.

“Conflict clarifies whose side you’re on. I think the strategy at the moment that is around delivery, which is necessary, but frankly, not sufficient,” Haigh said.

“What kind of government wouldn’t want to demonstrate delivery for their policy priorities? We need clarifying language, and we need to pick some battles and show by defining those battles whose side we’re on.”

She also predicted that it was “inevitable” Rachel Reeves, the chancellor, would have to put up taxes later this year to meet her fiscal rules and avoid further unpopular spending cuts that have alarmed Labour MPs and angered voters.

Starmer has found himself under fire from his own backbenches after losing his first byelection in government to Farage’s party by just six votes. Reform UK also won control of 10 councils, more than 670 council seats, and two mayoralties in a bad night for Labour and even worse for the Conservatives.

Labour is split about the best way to tackle Reform, with No 10 insisting it will go “further and faster” with its current plan while some of its MPs want it to change course. Jo White, a Labour MP and leader of the Red Wall caucus, called on Starmer to “stop pussyfooting around” and be more decisive on domestic policy, while the veteran MP, Clive Efford, said the idea the public want “more of the same is just nonsense”.

However, there is no agreement about whether the party should focus on trying to win back voters tempted by Reform’s rightwing populism or move to concentrate on cementing support from voters on the progressive left and centre.

Wes Streeting, the health secretary, defended the government’s approach to broadcasters on Sunday, saying it was not possible to “turn around a country in nine months” after it was left in a mess by the Tories.

“All I’d say to people is: we’ve got the message, we’re not daft, we haven’t got our heads in the sand. All I ask people for is a bit of time and to give us the benefit of the doubt … We are going at those challenges as hard and fast as we can,” he told the BBC’s Laura Kuenssberg.

Haigh, the most senior Labour MP to publicly criticise the party’s strategy yet, joined the ranks of anxious Labour politicians who have been analysing what Thursday’s elections might mean for them at the next election.

She warned that the party had to stop prioritising Reform-inclined voters at the expense of those on the left, saying Labour won the last election because it held together a broad coalition of voters from leftwing progressives to social conservatives by promising change.

“We have an absolute imperative to maintain the balance as we govern. It simply won’t be enough to go back to people at the next general election and ask them to vote for us purely so we can keep the Tories or Reform out.”

Ministers and Labour MPs are increasingly concerned that No 10 is not worried enough about the risk of losing voters on the left over issues from Gaza to welfare cuts.

A new poll for the public affairs firm Apella Advisors, conducted by Find Out Now, found last week that the threat of drifting progressive voters was significant. Among Labour 2024 voters, 43% said they would be likely to consider voting Green and 40% Lib Dems. Just 9% said they could consider voting Reform.

Farage was appealing to some Labour voters with a policy platform that was not exclusively rightwing, she said, with pledges to nationalise some industries.

The former cabinet minister suggested that a big economic offer at the spending review would give Starmer an opportunity to show those voters “they were listening”, while simultaneously winning over Reform supporters.

“Farage has been in the House of Commons recently with a steel nationalisation pitch, he favours water nationalisation. Reform voters, according to Hope Not Hate, are more in favour of banning fire-and-rehire than Labour voters are,” Haigh said.

Haigh called on Starmer and Reeves to change their rhetoric around the “trade-offs” between policies, as she fears it is fuelling voters anger around issues such as immigration, which she said was a symptom of people’s frustration at the “broken system”.

She said such language would allow people to “naturally conclude” that “there is no more money for pensioners or for welfare, but they [the Labour government] do have the money for [asylum seeker] hotels or they do have the money for international aid”.

A recent survey conducted by More in Common found that 67% of voters who were planning to back Reform UK at the local elections were driven to the party because their most important concern were “national policies on immigration”.

Hinting at the negative language about the economy that was used to justify difficult decisions such as the winter fuel cut, Haigh said: “I think certainly over last summer, I think there was pretty much a consensus now that we overdid it on the tough language.”

With Reeves under pressure from some Labour MPs to put up taxes or increase borrowing rather than opting for more spending cuts to balance the nation’s books, Haigh suggested that tax increases this autumn were inevitable given the economic backdrop.

“A changed approach to tax is almost inevitable, because I think without it we’re going to see the government keeping on coming back and making the same type of decisions as they’ve done around welfare on a very regular basis,” she said.

“You know, every time President Trump implements a new policy, implements a new tariff, changes his mind or something, it’s going to affect the chancellor’s headroom.

“We’re going to be presented with these very difficult and unpalatable choices again. So I think the likelihood of the current tax policy staying the same is highly unlikely.”

Many Labour MPs are privately furious about the government’s decision to institute sweeping welfare cuts, and the impact on child poverty, with the government’s strategy yet to be published.

Haigh said it was “obviously completely unacceptable” that child poverty is set to increase, according to the government’s own impact assessment. But she stopped short of saying whether she would vote against the contentious cuts to disability benefit payments.

“I do worry about a repeat to strategy that [could] mean we keep on cutting money from the sort of ‘bottom of the pile’. So many people joined the Labour party and were inspired by the work of the last Labour government on child poverty.

“The last thing any Labour government should do is create more poverty and push people actively into poverty.”

Haigh declined to discuss her departure from government – and ruled out any future leadership bid of her own.

However, she raised her concerns around the frequent briefings against her female cabinet ministers that she said “stifles debate” at the top of government.

“They’re being briefed against for their comments in cabinet; that’s not acceptable. Cabinet needs to be the space where people can bring their concerns and actively debate them. Otherwise, there’s frankly no point in them being at that table,” she said.

“I do think there is a particular issue among some [male] advisers against women, frankly, at the cabinet table.”