These threads are bonkers, so much mud slinging, so little content,
The tax credit system works like this:
Providing you work 16 hours per week, you get £3870 as a single parent or couple.
In addition, you get £545 for having children, plus £2690 per child.
If you or your child(ren) is disabled, there is extra money.
Everyone is entitled to this, but it gets withdrawn.
Tax credits get withdrawn when you earn over £6420 per year, at a rate of 41%.
You pay income tax when you earn over £8105 per year, and national insurance when you earn over £146 per week (£7592 per year).
Income tax is 20% and national insurance is 12%.
The national minimum wage is £6.19/hour, and therefore someone working 16 hours per week would earn £5150.08 in wages.
On top of that they would get £3870 in working tax credit, so effectively you take home not £6.19/hr, but £10.84/hr.
On £5150.08 you pay no income tax and no NI, and no tax credits are taken off you.
If you earn over £6420, as mentioned, they start to take the tax credits away, at 31%
On NMW this would be over 20 hours per week.
So on NMW, effective rates of pay with 1+ children:
Hours 0-16: £10.84 per hour
Hours 16-20: £6.19 per hour
Hours 20-23.5 £4.27 per hour
Then you start paying income tax, which is 20% as mentioned, so, effective tax rate is 51%:
Hours 23.5-25.5: £3.03 per hour
Then NI kicks in, so you are up to 63% 'tax':
Hours 25.5-30: £2.29 per hour
At 30 hours per week, they chuck another £790 of working tax credit at you.
So you've then got a choice:
16 hours per week NMW = £9,020.08 net (£10.84/hour, effective net)
30 hours per week NMW = £12,387.43 net (£4.63/hour effective marginal hourly rate above 16 hours per week)
Beyond 30 hours you lose more tax credits and there are no further bonuses, so the picture gets worse.
Also you get Housing Benefit, Council Tax Benefit, free school meals, and many other things that can make it irrational to work more hours.
It is of course hideously complicated, and a major deterrent to working more hours, because the net impact on your circumstances can be negative - you wouldn't more hours if it was going to make you no better off. Of course this tends to trap people in jobs with no prospects, but that's always going to be an issue when you pay any kind of means-tested benefits.
As I understand it the alternative is a citizens income scheme where each person is paid £x,000 per year, regardless of income. I believe this is a Green Party policy. If you work, you do not lose any of this, so there is no benefits trap as such.