A government scheme to help with energy bills is "underfunded by millions" and only helps a fraction of families at risk of fuel poverty, a charity has warned.

Save The Children said the UK Government's Warm Homes Discount scheme currently reaches just 3% of families at risk of fuel poverty.

The charity claims that energy companies have not committed enough funds to cover the 64,000 families it said should be eligible for the £120 rebate on fuel bills.

The "shortfall" means that only around 2,000 families would receive it, according to the charity.

Because tax and benefits policy is reserved to Westminster, it is the responsibility of the UK Government rather than the Scottish Government to implement the rebate scheme.

Douglas Hamilton, Save the Children's head in Scotland, said: "It's unacceptable that so many of Scotland's poorest families who need help heating their homes this winter will get nothing because energy companies have not put up nearly enough money.

"The scheme needs millions more or the cost will be counted in children's futures.

"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.

"We would encourage all parents who think they may be eligible for the warm homes discount to urgently contact their energy companies to make a claim."

Save the Children said one in five, or 179,000 children, are living in fuel poverty in Scotland, enough to fill Hampden Park three times over.

It said the number of fuel poor households with children rose by 40% in the last year - predominantly because fuel costs rose faster than incomes.

Save the Children is calling for the "big six" energy companies to ensure all families eligible for cold weather payments receive the Warm Home Discount.

This would provide support to at least 800,000 of Britain's poorest families, including at least 64,130 families in Scotland.

It is also calling for energy companies to transfer pre-payment meter customers, and customers in debt, onto the cheapest tariff, and for the government to invest in energy efficiency measures.

The Scottish Government backed the charity’s call.

A spokesperson said: "Save the Children are absolutely right to call on the energy companies to meet their responsibilities. In an energy-rich nation such as Scotland, no-one should have to choose between feeding their family or keeping warm.

"Scottish Government funding increases for fuel poverty and energy efficiency programmes contrast starkly with the dramatic reductions in the Warm Front programme in England. This year alone we have found an additional £7.1 million for fuel poverty and energy efficiency programmes, and will spend £55 million. Over the next three years, we will be spending around £250 million on fuel poverty and energy efficiency measures.

"The help is available to many more hard-pressed Scots than before, including carers, the most vulnerable disabled people and people who are terminally ill. The Westminster government is making significant cuts to its programme - from £350 million in 2010/11 to £110 million in 2011/12, £100 million in 2012/13, and down to nothing by 2014. From that point, there will be no UK taxpayer-funded fuel poverty programme in England."