I've beaten to the mark by the Adam Smith Institute. Like Madsen Pirie, I was struck as a I read Prospect that the write of their diary piece about the flat tax clearly hasn't a clue how it works:

If the threshold was set at £10,000, around 13m would have no tax bill. To raise, from the remaining 17m, the same amount of tax as was actually raised in 2004-05, the flat tax rate would need to be 31.5 per cent. Apply this to incomes of varying sizes and you find those earning £0-20,000 and over £60,000 end up better off, while the "hard-working families" on middling incomes lose out.

Duh. As Dr Pirie points out:

The idea that tax revenues are fixed, and that if some pay less others must pay more, is about as sensible as the 'wealth is fixed' outlook. The point of flat tax is that it broadens the tax base. People avoid less, evade less and declare more. Then they earn more. That is why a threshold of £12,000 and a flat rate of 22% raises more revenue than the present complex system of progressive rates and allowances.