News today that only 6% of the 200,000 new jobs created in the past year
are full-time, and part of the problem is that there are lower financial
obligations for workers who work less hours, why do employers not just
pay people cash in hand and tell them they must be responsible for their
own tax and NI?
I understand there is some issue with 'contractors' but I don't
understand it, but would it apply to a driver or a secretary, all the
commonly low paid jobs?

This has been quite a common issue already. That is why many has ventured to working from home businesses or the online marketing trade. At least through this, you are on your own. You even control and pay your taxes independently.

Online and homebased businesses are just as good as the normal office work of 8 to 5 daily, 5 days a week. Many have already venturend in to this kind of business. Anyone can try, somehow, in the end.. it can be as rewarding too.