Chancellor Rachel Reeves has urged an Andy Burnham-led government to stick to what she is doing because it is “beginning to bear fruit”, as she defended her handling of the UK economy.

The chancellor is backing Burnham to be the next prime minister, despite reports he could demote her to a junior cabinet position if he becomes Labour Party leader.

She said she would not pre-empt his choice of chancellor, but stressed that she had worked closely with him as mayor on “fiscal devolution” – transferring more powers to English regions – something he is committed to.

She told the British Chambers of Commerce (BCC) conference she was proud of her record so far but there was “more to do”.

Burnham looks set to replace Prime Minister Sir Keir Starmer, who announced he was standing down on Monday after losing the support of Labour MPs.

The former Greater Manchester mayor could take over as soon as 17 July if no other contenders emerge.

He is reported to be considering Ed Miliband, Wes Streeting or Shabana Mahmood as possible replacements for Reeves.

Some on the left of the Labour Party have called for Reeves’ fiscal rules to be relaxed to allow more spending on defence and other priorities.

These are rules are designed to ensure day-to-day spending is funded through tax revenue by the end of the Parliament, only borrowing for capital investment and reducing debt as a proportion of GDP.

But Reeves told the BBC Conference: “Andy has been really explicit – he backs those fiscal rules.”

She claimed she had brought “stability” to the economy since becoming chancellor and added she was “proud” of her record on inflation and growth.

“Yes, there is more to do,” she told Sky News journalist Sophy Ridge, who was hosting the conference, saying the budget later this year would include further reforms to business rates and fiscal devolution.

But she added: “I hope that whoever is chancellor, in the future… sticks to what I’m doing because it is beginning to bear fruit.”

Asked whether she accepted there needed to be a change at the top, Reeves said: “Clearly we need to do more to connect to the country to tell a better story of what we’ve done in government but also set out the vision of where we want the country to go.

“That is what Andy will be able to provide as our next prime minister. He is a great communicator, he’s got a great track record of delivering in Greater Manchester, and I have no doubt he will bring that to the position of prime minister.”

Burnham is so far the only contender to replace Sir Keir Starmer, who announced his resignation earlier this week following a slew of senior cabinet resignations.

If no other challenger emerges, Burnham could become prime minister as soon as 17 July.

In an earlier interview with the BBC, Reeves said: “The last government lost control of the public finances.

“It sent inflation through the roof and interest rates through the roof. So control of the public finances has a real impact on families today.”

While Reeves said she had improved the flexibility in the government’s budget by increasing its financial headroom, she added the public must be left in no doubt about the party’s commitment to fiscal discipline.

“Because if you lose control of the public finances, it is ordinary working people and businesses who pay the price with higher inflation, higher taxes and indeed higher interest rates,” she added.

The chancellor was absent from the crowd outside 10 Downing Street on Monday as Sir Keir announced he would be stepping down as prime minister, but was present for a group selfie with Burnham following his swearing-in at Westminster later the same day.

Reeves said no one could doubt her commitment to Sir Keir, but when pressed on her absence from his speech she would not be drawn on why she had not been present.

“I don’t think anyone can doubt my commitment to the prime minister. I’ve been by his side for six years now as shadow chancellor and then as chancellor of the exchequer,” Reeves said.

Reflecting on her time as chancellor so far, Reeves acknowledged there were things she could have done better but said she was “really proud” of her record which included increasing the national living wage and national minimum wage, and seeing the economy grow and inflation flatten out.

“I know that whoever is prime minister and chancellor in the future will inherit a stronger economy than the one I inherited two years ago,” she said.

Conservative shadow chancellor Mel Stride, also at the BCC conference, said a potential Burnham government should rule out additional tax rises on businesses, which he described as already “overburdened”.

When asked whether he wanted a general election to be called, he said the country needed a “clear plan from an incoming new regime that they understand business and they’re going to take the right kind of decisions to get the economy moving”.

Liberal Democrat leader Sir Ed Davey told the conference the UK needed closer ties to Europe in order to deliver growth for the economy, including by rejoining the single market and customs union.

He would not be drawn on whether his party may consider a coalition with a Labour Party led by Andy Burnham after the next general election.

“I’m very confident about when my party is going to be. It will be, I think, Mrs [Kemi] Badenoch who will be worried about questions about coalition,” he said.

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