Total outstanding government debt in the UK has risen to a record £799bn, or 56.6% of UK GDP - the highest since records began in 1974.
New borrowing in June was £13bn, almost twice as much as a year ago, the Office for National Statistics said, after the downturn shrank tax receipts.
The figures also reflect the cost of bank bail-outs and higher spending on social security benefits.
One economist described the state of the public finances as "dire".
"The figures are modestly better than expected. It doesn't take away from the fact that the state of public finances is dire and that a considerable degree of fiscal tightening will be required," said Philip Shaw, chief economist at Investec.
The question bankers, business people or politicians ask more than any other is whether the government will be able to borrow all it needs from markets
Business groups warned that, although it appears that public borrowing is in line with the chancellor's forecast, the government must not sit back.
"It would be wrong to tighten policy while the recession continues, but maintaining Britain's international credibility requires a robust plan for restoring our public finances over the medium-term," said David Kern, chief economist at the British Chambers of Commerce.
"This must focus on curtailing public spending across the board, while avoiding damaging measures that would harm wealth-creating businesses."
Meanwhile, a National Audit Office (NAO) report said that tax receipts fell by 10% in the past year - the biggest fall since 1923.
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