"people managed on what they earnt when we were young"
Nope. The benefits were just called different things. National Insurance started in 1911, and there was certainly dole from the 1930s or earlier.
And even with these benefits, from the family history I've been doing, I can say people often didn't survive very well.
I've seen children abandoned in orphanages because one parent absconded and the other couldn't afford to keep them. That was c1920.
I've seen a woman, abandoned by her husband, taking up with a man who abused her children, because it was a way to get bed and board. She died young, probably hastened by malnutrition and poor living conditions, leaving her 6 children to more abuse. That was 1960s.
More generally, childcare was done by older girls, who were expected to leave school to look after the little ones (see socio-political writer Winifred Holtby's 1936 novel South Riding ).
Indeed the school leaving age was only raised to 15 in 1944, and to 16 in 1972. At the start of WWII, children from poor families were expected to be working full-time at 14 or doing housework so others could work.
It just took one serious illness or death to drive a whole family under financially. And that's before you take into account cocklodging bastards of the sort who even now fill the Relationships threads. They were no thinner on the ground then, and the impact on women and children was vastly greater.