I do not know the *statistical facts*, Deskdiary, but I sense that this is what you are after. If you already have access to these then please save us the effort of googling them for you ;-) (and I do wonder why AB even exists, in a world well equipped with search engines *except* when it is conversations and opinions that you really seek).
Two simple 'facts' I will offer, in lieu of an answer:
1) Population is always increasing, even before you add immigration. It might be necessary to always keep in mind who was in power 10 or so years prior to any given Labour government. If it is the case that economic booms lead to baby booms then governments 15+ years later will be faced with billing the nation for the education bill, boosting infrastructure and so on.
Youth unemployment is a serious blow to business: they should be growing their music collection and equipping their first flat, not scrimping and saving to get by. Belt-tightening is bad for business. After a recession gets Labour booted out, the next boom just falls into the Tories' lap. It's all in the timing.
2) I thought it was employers who ultimately control unemployment? Governments can grow or shrink the Civil Service, the NHS, the emergency services, the Armed Forces and very little else. They have control over employment levels other than that.
If I can find it, I'll post a link to "A Brief History of Corporate Whining", which repeats the typical excuses given for companies not lifting too many fingers to alleviate unemployment (they blame government regulations, mainly).