Britain's national debt has risen above £1tn for the first time on record, underlining the huge task facing the government in bringing the public finances under control.

Official figures released on Tuesday morning showed the total public sector net debt (excluding the impact of the 2008 banking bailouts) rose to £1.004tn in December, the highest since records began in 1993 and equivalent to 64.2% of GDP (up from 59.4% a year ago).

The government claimed that the milestone underlined the need to cut Britain's borrowing levels.

"[This] shows the unsustainable level of spending this country built up over the past few years, and shows why it is critical for our nation's future that we deal decisively with the deficit," a Treasury spokesman said.

Daniel Solomon, of the Centre for Economics and Business Research, said at least the government's focus on fiscal prudence had resulted in low interest rates on its debt. "A UK 10-year government bond now has a yield of 2.2%," he noted, "although, in signs that markets don't find the UK's debt reduction policies entirely credible, this figure has risen over the month."

There was some good news for the chancellor, George Osborne, as public borrowing is down for the current financial year, putting him on track to meet his targets. The government borrowed £2bn less in December than a year earlier, as the bank levy boosted the public coffers and spending fell slightly.

The Office for National Statistics said public borrowing, excluding banking bailouts – the government's preferred measure, fell to £13.7bn last month from £15.9bn in December 2010. The government has borrowed £103.3bn in the fiscal year so far, down from £114.6bn at this stage last year. Government receipts climbed 7.3%, boosted by the VAT increase to 20% from 17.5% a year ago, while spending fell 0.9%.

Most City analysts reckon the chancellor will achieve his target of reducing the budget deficit to £127bn, or 8.4% of GDP, this fiscal year, from £136bn last year. But this is at risk if the eurozone takes a turn for the worse, or Britain slips back into recession. GDP figures out on Wednesday are expected to show the UK economy shrank by 0.1% between October and December.

Vicky Redwood, senior UK economist at Capital Economics, said Tuesday's data showed the government borrowing for the current financial year was still coming in "comfortably" below last year's total. She warned, though, that the £1tn debt figure was a "reminder of the enormity of the challenge that still lies ahead to get the public finances back on a sustainable footing".

Similarly, Nida Ali, economic adviser to the Ernst & Young ITEM Club, warned: "The longer term outlook remains very uncertain and the recent strong trends will be increasingly difficult to sustain.

"With the eurozone crisis showing no signs of abating, it's possible that the Office for Budget Responsibility's growth forecasts will prove to be too optimistic, despite significant downgrades in November. This will have adverse implications for the public finances and the chancellor could have some more difficult decisions to take when he presents his budget in two months' time."

Including the cost of bailing out Lloyds Banking Group, Royal Bank of Scotland and Northern Rock, as well as some revenues from the banking sector, public borrowing came in at £10.8bn in December, down from £13.9bn a year earlier.

Rachel Reeves, Labour's shadow chief secretary to the Treasury, said: "The government is only on course for borrowing targets that are already a staggering £158bn off track, meaning David Cameron and George Osborne's promise to balance the books by 2015 now lies in tatters. This £158bn of extra borrowing is more than £6,500 for every household in the country. And it's the bill for economic failure and a growing dole queue, rather than to help create jobs and support the economy through difficult times.

"Of course we need tough decisions on tax, spending and pay to get the deficit down but it's also vital we get people off the dole and into work. More people out of work on benefit just makes it harder to get the deficit down. It doesn't make economic sense.

"The government needs to change course and adopt Labour's five-point plan for jobs, to kick-start our flatlining economy and so get the deficit down in a fairer, better way."