One of Andy Burnham's economic advisers has urged Labour to borrow more - sparking fresh fears about Britain's debt mountain if he enters Downing Street.

Jim O'Neill, co-president of the Northern Powerhouse Partnership and a former Treasury minister, called on the Government to be 'bolder about borrowing to invest'.

He suggested more could be done to 'explore' Chancellor Rachel Reeves' fiscal rules in order to boost spending.

'I think the second part of the fiscal rule on borrowing to invest I think that could be explored a lot more, and not in a way that freaks out the financial markets,' Lord O'Neill told Sky News.

The crossbench peer added: 'I don't think you'd necessarily have to rip up the fiscal rules. I think you just need to be bolder about borrowing to invest.

'A lot of people right now, given Britain's history for 30 years or more, think any kind of borrowing just means wasted money.

'But if you borrow for things that have really positive multiplier effects.'

There is a widespread expectation that Mr Burnham will become prime minister in the coming weeks following his thumping win in the Makerfield by-election.

Keir Starmer has vowed to fight any leadership challenge and insisted he will not 'walk away', but a large number of Labour MPs are demanding he now swiftly hand power to Mr Burnham.

Lord O'Neill, the co-president of the Northern Powerhouse Partnership who served in George Osborne's Treasury team, was recently revealed to be among three economists Mr Burnham had drafted in to boost his team of advisers.

Mr Burnham is also said to be receiving advice from Andy Haldane, a former Bank of England chief economist, and Richard Hughes, a former chair of the Office for Budget Responsibility.

Lord O'Neill's comments prompted fresh concern about the parlous state of Britain's public finances under Labour.

Senior Tory MP Andrew Griffith, the shadow business secretary, told the Daily Mail: 'Debt is already out of control with money that should be spent on defence, instead going to pay the interest.

'It's time for hard choices, not more dodgy accounting and higher borrowing.' 

During his successful campaign to become Makerfield MP, Mr Burnham called for Britain to abandon '40 years of neoliberalism'.

This prompted claims that he and Ed Miliband - his potential pick as Chancellor - plan a radical economic agenda for the country.

UK gilt yields, which determine the cost of Government borrowing, rose on Friday after Mr Burnham's victory in Makerfield cleared the way for his expected bid to oust Sir Keir.

The yield on 10-year gilts ticked up to 4.84 per cent at the time of the London equity markets close on Friday, compared to 4.76 per cent at the same time on Thursday.

Kathleen Brooks, research director at XTB, said: 'Andy Burnham may have won a resounding election result in Makerfield last night, but he has hard work to persuade financial markets that he is the right man for the job to grow the UK economy and get debt back under control.'

However, Ms Brooks noted the rise in yields was not all down to Mr Burnham's win, as figures showed Government borrowing costs topped forecasts in May.

According to the Office for National Statistics on Friday, public sector net borrowing, excluding public sector banks, totalled £23.3billion in May, up 30 per cent from £17.9billion a year earlier.

The figure exceeded the £17.7billion forecast by the Office for Budget Responsibility by £5.6 billion.

Ms Brooks said the rise in UK gilt yields tells 'us three things, one, it is not all because of Andy Burnham, two, you cannot borrow excessive amounts of money when growth is flat-lining, and three, Burnham faces extremely constrained circumstances if he does topple Starmer'.

Should Mr Burnham become PM, JPMorgan analyst Allan Monks sees a 'high risk' that he would consider a change to the fiscal rules, despite appearing to rule this out in recent weeks.

'He would need to tread carefully given market pressure, but a change motivated to allow more growth-enhancing investment spending could work if communicated in the right way,' he said.

'This would receive some support from a range of economists and think tanks.'

The UK's public sector net debt currently stands at around £2.9trillion, which is equivalent to £100,000 per household.