The estate down the road from me has a great local community enterprise with a cafe and shop selling things very cheaply. Their produce is surplus or short date items and donated by local supermarkets
We have schemes like this locally, except the food is given away free rather than paid for, in big bags of 2-3 days worth of food. People were turning up there daily demanding bags (despite having had one the day before, and before that) or bitching that the stuff is short date, or foods their kids don't like.
Likewise I know a few people who have volunteered to make (and deliver, before anyone pipes up about travel costs) dinners to families this week, and local businesses. Zero take up. What does that tell you?
The reality is that not everyone receiving benefits classes themselves as in poverty, some people are able to manage and live to an acceptable standard. Clearly some are not. But throwing more and more money at it, in isolation, won't help, especially not for those parents who don't or can't currently prioritise their child's needs.
You could give more money as food vouchers redeemable at local supermarkets. Might help, except the response is then 'but what about all the people without a local supermarket - that food money won't go as far there?'
Or maybe you offer free supermarket deliveries (I know Iceland already does this - yes you have to spend £40 but most people spend about that a week I think?) Although arguably if you're spending only £40 a week or less it's easy enough (unless you have a physical disability) to carry that amount of food home on the bus, or even on foot if your supermarket is in walking distance. I've never got a taxi home with my shopping although a neighbour of mine did it all the time. Why spend £10+ on taxis when the bus is £1.50? (disclaimer - I accept not ALL buses are so cheap, and some people don't live in reach of a bus).