"Labour came to power owing nothing" is completely misleading. Debt as a % of GDP was around 38% when they came to power, it fell in the first few years but has risen and currently stands at about 37.8% - not too high (and excluding NR which is scheduled to be paid back - though there is a risk it will not be.
the alleged problems are it is forecast to rise to over 40%, though this is still not too high and not as big a problem as made out in the media. Under Lamont, for example, it rose to >45%
They raise this money by issuing Government Bonds, Gilts, etc which anyone can buy