Papaumau, The main problem now regarding a minimum wage is the means test for housing benefit and council tax exemption.
How many workers by receiving a pay rise ( minimimum wage), would find themselves over the threshold for the above help, and therefore be worst off having to pay high rents and council tax.
What we need before anything else in this country is a national council house building programme, and to get rid of the council tax by replacing it with higher taxes on middle and high earnrs.
With abolition of the council tax in favour of a local tax based on ability to pay and higher income tax rates, there will be winners and losers among middle England, but this is better than a form of local tax not based on ability to pay.