Some of the UK’s poorest families are not getting the help they need to heat their homes this winter from energy suppliers because of a funding shortfall, a leading charity has warned.

Save the Children claims a national government-run scheme set up to help with household bills had reached just 3% of families at risk of fuel poverty because energy companies have not committed enough funds to support vulnerable customers.

According to the charity, 800,000 of the poorest families who get cold weather payments should also qualify for a £120 discount on fuel bills under the Warm Homes Discount scheme, but a huge funding shortfall means only 25,000 families will get it.

Its research shows that growing up in cold, damp homes can slow children’s development, worsen long-term problems like asthma, and lead to rises in hospital admission rates.

The charity’s No Child Left in the Cold campaign is calling on energy companies and the government to fill this funding gap, so more families are given the fuel discount. It also urges companies to better promote the scheme to low income families.

The Warm Homes Discount scheme grants a rebate to eligible households of £120 in the first year (ie winter 2011-12), £130 in year two, £135 in year three and £140 in year four on their energy bills.

But the charity says it is fundamentally flawed because the government does not require the energy companies to provide enough funding to support all households on low incomes and at risk of fuel poverty.

It said: “Despite research which shows the risk of living in fuel poverty is almost the same for low-income families as it is for pensioners, the government has decided that only poorer pensioners will form the ‘core group’ automatically eligible for support.

“The ‘broader group’ are eligible for – but will not automatically receive – the discount because payment is at the discretion of each energy company.”

Save the Children’s chief executive officer Justin Forsyth said: “It is unacceptable that 97% of the UK’s poorest families who need help heating their homes this winter will get nothing because energy companies have not put up nearly enough money.

“Without this help the choice for parents is stark: cut back on food, get into debt or risk their children’s health because they can’t afford to keep them warm. The scheme urgently needs millions more from the energy companies, or the cost will be counted in children’s futures.”

Almost a third of low-income parents (earning less than £12,000 and deemed to be living in severe poverty) with children under 16 polled by the charity said they won’t be able to afford their winter energy bills, almost half (45%) said they were considering cutting back on food in order to pay their bills, and only 9% said they had heard of, and were planning to apply for, the Warm Homes Discount.

A spokesperson for the Department of Energy & Climate Change (DECC) said about 2m homes were set to get discounted bills under the Warm Home Discount scheme, significantly more than under the previous voluntary scheme. “This year, suppliers will be required to spend up to £250m – that is 40% more than last year. We hope energy companies will strive to help all their customers that qualify.

“But we’re also focusing on the causes of fuel poverty – in particular poor household energy efficiency. There is free and cheap insulation available to low income households from energy suppliers and the Warm Front scheme, and this will be also be a core feature of the new Green Deal from the end of the year.”

Christine McGourty, director of Energy UK, said: “Far more than 25,000 families will get help from their energy companies this year. Almost £180m was spent last year on voluntary schemes to help nearly 2 million of the most vulnerable customers, and that figure will increase to £250m this year.

“Following consultation, the government decided who will benefit from core funding under the new Warm Home Discount scheme, and those customers will get an automatic discount off their electricity bill without the need to apply for it. A wider group of 650,000 people by 2013-14 will also benefit.

“All the major energy companies have been writing to their customers this winter promoting the help that is available and all of them fund the free and independent Home Heat Helpline advice service on 0800 33 66 99. It’s important that families stay warm this winter and anyone who is worried about paying their energy bill should get in touch with the helpline.”