I suppose 2 adults working 30 hours each is equivalent to one working full time 40hours and one working part-time 20 hours which is not a crazy thing to do with 3 children to manage.
In fact you are probably better off as you likely pay less tax the way you are doing it.
I think private rental is a huge problem for so many people. It just costs far too much as a percentage of income and does not allow people to save for a deposit.
I don't love my house but it's all owned and mine so costs me zero per month apart from all the maintenance etc. I had help from my parents though to buy in 2014 when prices were still quite low. Now I'm looking at moving in the next 12-24 months and house prices to buy are totally shocking. My house cost 197K in 2019 and is now 'worth' over 250K. Now for me going from one house to another it probably makes no difference as I'll just be selling at a high price and buying at a high price. For people who are not yet on the market though that's a huge jump in a few years.
The only people I can see the benefit from rising house prices are people who sell without buying (death sales or sale of additional properties). For the rest of us there is no benefit but it costs more in stamp duty etc to move as these are based on house values. So i suppose the goverment benefits.
OP - my recommendation and I don't suppose you can do it would be to buy anything even if it is a 2 bed flat (and yes that would mean sharing rooms and potentially the livingroom being doubled up as a bedroom).
It would be utterly crap for a few years but it would break the cycle of paying huge amounts of private rent and getting nowhere. It might even let you save a little each month for the future.
There are mortgages now where you can borrow almost the full amount. Do you have anyone that could lend you a small deposit (a parent?)
My house is a 3 bed (ha, 2 tiny doubles and 1 single) and not particularly huge. People renting similar sized houses here in town in Scotland are paying about £1400 too. It must be soul destroying to pay that much each month.
The reality is we need more children being born to balance out an ageing population. If something could be done about the housing market more people would be able to afford more kids.
Worrying times.
OP just bear in mind that your benefits may be cut at some point given the state of the country and the increasing unaffordable UK debt.