The official poverty line is half the median wage around £15000 per year an older person or couple could usually manage on that, the problem is single parents or couples with children, especially when employment is difficult. By far the largest cost is housing, rents are far too expensive, to pay the rent, food is got from food banks and of course if free food is available it will be used. Rents need to be controlled no doubt, it is very hard for councils to find suitable accommodation for everyone, controlling rents will make that worse.
Homelessness is a different issue, relationship breakdown depression and mental illness are the factors here, poverty line is not relevant if you’re living on the street. Of course we need more hostels.
There are always going to be a large proportion of children in poverty because the level of single parent families is so high, no government is going to cure that, certainly not the Tories.