I think again the biggest issue is why in-work income support should even be needed. I'm not talking about part time work, or any exceptions.
When I started work back in the early 80's, a basic job could be enough to support a family of 4. Roll on to today, it's barely enough to support one person without help from somewhere. Start thinking about your own household bills, ignoring for the moment housing cost as it's so different between mortgaged and rented. Typical food for the week, utilities, essential travel, essential clothing as you can't go to work naked or in completely knackered clothing or shoes. Other household essentials like phone, internet, cleaning products, council tax, insurances.
Then add in those housing costs. If you have children, a 3 bed house isn't a massive luxury. There are very few places in the UK, especially where there's half decent infrastructure, where you can rent for under £1000 - £2000 per month. On £30k pa assuming standard 5% contributions to pension, you're taking home £2k per month. If both parents work to increase income, then feed in child care costs
THIS is why people need to claim in-work benefits.
And don't suggest getting a better paid job! Just think of the screams if you try to call public services and there's a 5 hour wait on hold because nobody wants to do the low paid job. Care workers, who look after the elderly and disabled, are on minimum or close to it. Street cleaners, shop workers, baristas, hotel & bar workers, Amazon warehouse operatives, road menders, all of these are on lower wages and we can't do without them.