For what it is worth, I wrote a short policy paper on the minimum wage for a Public Policy Economics class.
tl;dr version: The Minimum wage has distortionary effects on the labor market, no getting around that. An expansion of welfare provisions (as in actual welfare payments as opposed to 'workfare') would be able to replicate much of the benefit of the minimum wage with fewer distortionary effects. That said, I don't trust either political party enough to create and maintain welfare spending at a level sufficient to replicate the effects of the minimum wage, so in most respects the minimum wage is the best of an altogether poor situation.
I imagine one way around it would simply be to pay all unemployed people £7 per hour - at which point, wages would have to rise, and that cost would be borne by the employer rather than (as with in-work welfare) the taxpayer alone.