But morebeta - what about a LONE PARENT family with 2 dc? They will still need the same size house, the same utility bills, HIGHER childcare bills (as no other parent to look after the dc), yet by your calculations, they would only have a tax free income of £20K.
And NONE of that allows for the fact that a FT minimum wage job DOES NOT COVER YOUR ESSENTIAL OUTGOINGS.
Just because that £10K would be tax-free, it doesn't mean that it will stretch to cover your rent, council tax, childcare, utilities, travel to work, clothing and food, does it?!
Unless you are aware of some way of making £10K stretch further than I can? My 2-bed, mid terrace HA house costs £6,259pa. Which out of a £10K income leaves just £3,741pa for everything else. My Council Tax is another £1,332pa. Leaving £2,409pa. My electric bill is around £1,000pa. Which leaves £1,409pa. My Gas bill is around £400pa. Leaving £1,009pa. My water bill is £350pa. Leaving £659pa.
So I am left with £659pa to: Pay for childcare. Pay for travel to work. Pay for clothing. And, oh yes - pay for food too!
And THAT is why £10k is NOT enough to live off without State top-ups.