Well, its quite a mixed story if you look at the UK national debt - no where near as simplistic as is being suggested here.
The IFS give national debt as a % of GDP from 1900 up to 2000 in figure 3 here. The ONS has debt as a % of GDP from 97 here. Looking at it it would seem that debt fell fairly steadily as a % of GDP from the war until around 1980, then plateaued. It then fell steadily from 1997 until 2003, when it rose again - but only to the level of around 1998 - then rose dramatically with the onset of the financial crisis.
So it would appear that from 2003, Labour moved back to the level of debt as a % of GDP that had been maintained by the Conservatives in the 1980s.
Should point out that I am no fan of Gordon Brown - but I do think that there is a somewhat hysterical anti-deficit movement at the moment. I keep linking to Paul Krugman's blog, but he does have lots of interesting things to say on the subject. Anyway, must cook dinner, back later, flame me as you will