A Wakefield Council report said that almost 20,000 local children were living in families facing real "financial hardship".
The numbers date from 12 months ago, meaning the reality is likely to be worse, as jobs lost at the end of the furlough scheme and spiralling inflation in recent months weren't taken into account.
In the Wakefield Parliamentary constituency, 35 per cent of children were classed as living in poverty. In both the Hemsworth and Normanton, Pontefract and Castleford constituencies the figures were 31 per cent.
Labour councillor David Jones, the chair of Wakefield's children and young people scrutiny committee, said rising energy bills and the National Insurance increase would soon make it even harder for households.
He warned: "I think it's going to get worse before it gets better, because of all the cost pressures that are coming to bear for families.
"What I'm hearing from some people in my ward now is that they can't even afford to travel to work. It's that bad.
"I think we're on the cusp of something really worrying."
Coun Jones, a councillor for Pontefract South and a former head teacher said a lot of old "assumptions" about poverty no longer stood.
He said: "You can't assume it's just families living in poorer areas. We've got a squeezed middle that I suspect will get bigger
"With Covid and children being sent home from school, it became quite clear that not every family had the internet and not every family had a computer.
"I think there's been a blanket assumption for a while that everybody's got everything like that, when the reality is they haven't.
"I think as an authority we're doing a lot (to help people), but there's outside factors that are making poverty worse."
Households earning less than £17,760 a year - currently 60 per cent of the average UK salary - are defined by the government as living in "relative poverty".
Those with an income of less than £15,660 per year are classed as being in "absolute poverty".
The council report, which will go before a scrutiny committee next week, added that kids in living in inadequate housing were more at risk of respiratory problems and even meningitis.
It added that: "Those in the most disadvantaged areas can expect 20 fewer years of good health in their lives than children with more resources."
Local Democracy Reporting Service