Frank Field is demanding Government action to provide comfort for 6,000 children in the town who are missing vital support to keep their homes warm.
The Government's "Warm Home Discount" scheme requires large energy companies to take £135 a year off poor households’ energy bills.
But the Children's Society has found that nearly 2m poor families with children – representing more than half of all children living in poverty in Britain – are not covered by the scheme because different energy companies use different eligibility criteria for the discount.
Mr Field said: "The costs of fuel, food and housing have taken ever greater chunks out of people's incomes for almost a decade.
"This has been a disaster for poor families, particularly for those with children.
"Extra support towards paying the energy bills can make a real difference to the wellbeing of poor children by helping to cover the cost of living, but the energy companies are letting them down."
Mr Field has written to Energy Secretary Ed Davey demanding answers on how the Government plans to improve the scheme to ensure all those who should benefit from the scheme are able to do so.
He added: "It should be the government's job to make sure the energy companies step up and do their bit to ensure poor families are not forced to live in cold homes.
"That's why I’m urging Ministers to implement a standard set of rules for all energy companies involved with the scheme, which learn from those currently in place that are the most fair to poor families making an application."