Because not every family CAN have 2 ft workers. And there ARE lots of people on minimum wage in the SE. And it's no longer most houses that have 2 incomes coming in - it's only about 55-60% if I remember rightly (can't remember where the heck I saw that fig, sorry). So 40-45% of houses either have one income due to SAHP or one income due to LP or one income due to disbailities that are too bad to work FT, but not bad enough to get DLA.
Why do you seem to think that a shop assistant in the SE gets paid more than a shop worker in the NE for example? Minimum wage is the same countrywide. So how can there be 'not that many' minimum wage workers in the SE?
OK some cultures in the UK may have 4 earners/ different family patterns, but it's not the norm for a lot of people, they have 1/2 FT workers, and may only have a household income of £12-£24K pa (£12K is minimum wage FT, not £13K, so £12K for one earner, £24K for 2 ft earners).
There are PLENTY of people in the same/similar situation to me in the SE - Take for example, a couple with 3 dc, two of whom have disabilities - one FT worker, other in receipt of carers allowance - which you only get paid for one, not 2, so around £53/wk. So if the FT worker is on min wage, and you add on the 'income' from CA - It certainly wouldn't cover every cost needed to survive above poverty level.
What if you don't have the potential to earn £20K? Not everyone does, you know - shop managers in my SE town are paid £14-£17K pa, and not everyone is capable of being a shop manager!