The economy was always going to recover eventually - they always do. The problem is that the growth we're only just starting to experience (while it is welcome news) is comparatively pretty modest, and has been severely delayed and limited by the government's badly-thought out austerity measures.
It's a very common idea - being pushed by the government, and lapped up by the press - that the British debt situation is catastrophically dire due to years and years of Labour overspending, and that we have no choice but to cut spending which has quite a severe impact on peoples' lives.
This is a powerful idea, but unfortunately, the reality just doesn't seem that simple. British debt history prior to the credit crisis was, within expected parameters, pretty stable after the late '70s and didn't change all that much based on whichever party was in office. It spiked during the crisis because of the bank bailout (which most people seem to agree saved us a great deal of pain in exchange for putting up with a horrendously unjust treatment of those responsible for the mess).
http://krugman.blogs.nytimes.com/2011/12/04/british-debt-history/?_r=0
http://www.telegraph.co.uk/finance/budget/9932748/Budget-2013-Britains-debt-and-deficit.html
Labour largely inherited Conservative economic policies and preserved them - they really didn't differ a great deal so it doesn't really make sense to say that the current debt situation is some kind of particularly Labour legacy.