Andy Burnham has instructed the Labour party to “re-arm” to fight the Conservatives at the next election amid concern inside government that they must take the prospect of a Kemi Badenoch-led recovery seriously.

Downing Street sources said the prime minister wanted Labour headquarters to refocus on the Tories as an electoral threat after more than two years of prioritising Nigel Farage’s Reform and – on their left flank – the Greens.

“Andy is well aware of how volatile electoral support is. Just because the Tories are trailing in the polls now, their trajectory is upwards and they could bounce back ahead of the election. We can’t be complacent about our old foe,” one source said.

The Conservatives took 24% of the vote at the last general election, before support dipped to 18%. But last week this had risen to 25%, according to polling from More in Common, the first time in 18 months they have exceeded their vote share at the time of their record election defeat.

Many Tory MPs, who had felt that their party’s situation was existential, now believe they have a route back, with Badenoch finally appearing to recognise that the economy, rather than culture wars, presents her with an opportunity, especially with her core vote.

A senior Downing Street figure said that Burnham did not want party officials to take their eyes off Reform – which has dipped in the polls amid ongoing scrutiny of party finances – but felt they should be planning for a potential Tory resurgence as well.

A third No 10 insider told the Guardian: “Kemi is running a party base strategy with policies aimed at higher earners, mostly in the south. It won’t be enough to win them at the next election but it does put them more in contention. We need to be ready for that. We need to re-arm.”

Cabinet ministers including transport secretary Heidi Alexander, chief secretary Emma Reynolds and Europe minister Hamish Falconer all have Tory-facing seats, while Labour MPs across Hertfordshire, Kent and parts of London, including Finchley and Harrow, could also be at risk.

One tactic under discussion is talking up the prospect of a Tory-Reform pact, with MPs suggesting voters would only return in earnest to the Tories if there was a genuine chance they could win a majority, but that they could stay Labour if they worried about Farage getting close to power.

Another is to focus on the Tory brand – including the shadow cabinet – more generally. While Badenoch’s personal ratings are relatively strong, the Conservatives overall lag way behind, with a third of people who told More in Common she was doing a good job, still saying they would not vote for her party.

Labour officials insisted that, as the Conservatives were the official opposition in parliament, they still had them in their sights day to day. But they acknowledged they needed to step up their strategy more generally.

The party is understood to be preparing to devote more resources to taking on the Tories from January, in the run-up to the next May elections. “We did really well at this set of elections last time, so it will be a real test point for whether the Tories have got their act together,” one said.

A group of London MPs has personally urged Burnham to refocus on Badenoch’s party, which in some polls has overtaken Reform into second place, warning him that Labour HQ was “getting caught out” by “obsessing” about Reform and the Greens.

One minister with a slim majority said they had been raising the alarm inside government about the need to refocus on the Conservatives.

“I have been banging this drum for a while. It’s time to wake up about it, frankly. I think lots of my colleagues under threat from Reform have seen some of us in more traditional Tory seats as having it easy but by the next election it could be the other way around.”

One former Keir Starmer staffer said: “Every arm of the Labour party has been refocused to take on Reform, all the strategic decisions have been taken with that in mind. That can change if the party starts the work now but it does need to start properly.”

Luke Tryl, director of More in Common, said that Burnham was right to broaden the party’s focus. “Starmer was fighting on one front, but Labour now has two fronts on its right flank. They need to prepare for all outcomes,” he said.

“Reform has shown an ability to squeeze the Conservatives but it definitely has limits, so they’re definitely going to be on the pitch at the next election.”

Tryl suggested that the biggest risk to Labour was “self-sorting” by voters, with Reform winning right-leaning votes from Labour in the “Red Wall”, while the Conservatives took them in affluent parts of England including the south-east.

“Because of the shallow but broad nature of Labour’s support at the last election, there are more seats that could end up being Labour-Tory fights than you might think,” he said, adding that the Tories were also currently taking more votes from the Lib Dems than the other way round.