British Gas is to donate 10% of its profits to help customers cope with soaring bills for the "duration of the energy crisis".
Its owner Centrica says the money will go into an existing support fund - trebling help available this winter for the poorest customers.
The firm, which has seen huge profits this year, said thousands of households would get grants of £250-£750.
But this is a fraction of the support needed to tackle the crisis nationally.
Earlier this week, one energy company boss put that cost closer to £100bn.
British Gas' offer of support will be based on the company's retail supply profits, which were £98m before tax in the first-half of 2022. It said the initial donation would be £12m.
However, Centrica, which is the parent company of British Gas, reported adjusted operating profits of £1.3bn in the six months to June - up from £262m a year earlier - most of which came from oil and gas drilling.
And Paul de Leeuw, director of the RGU Energy Transition Institute at Robert Gordon University in Aberdeen and a former executive at Centrica, British Gas's initial donation would only benefit 0.5% of its 7.5 million customers.
He told BBC Radio 4's Today programme that while it was a helpful gesture, the initial £12m donation amounted to just 1% of Centrica's profits.
"They've got 7.5 million [residential] energy customers in the UK, so if you look at the money that is available, it's probably going to benefit around 40,000 people max so that's 0.5% of their customer base.
"So 99.5% of Centrica and British Gas customers are probably not going to see any benefit from this."
At-a-glance: What British Gas is offering
- British Gas customers in fuel poverty and with less than £1,000 in savings are eligible
- A household is considered to be in fuel poverty if it has to spend 10% or more of its income on energy
- Eligible customers can apply for a one-off grant through the British Gas Energy Trust
- Since its creation last year, British Gas said "thousands" of customers received average grants of over £550
- Over a third of the recipients were on disability benefit, 30% were single parents and 25% had children under five
It comes as the next energy price cap - which limits what suppliers can charge per unit of energy in England, Scotland and Wales - is set to be announced on Friday.
The typical home energy bill is forecast to reach £3,600 a year in October - up from £1,971 currently - with further rises expected for January.
The government has promised a package of help but there have been warnings many people will face hardship without further support.
Energy firms are also under pressure to help after posting soaring profits this year, amid record high energy prices driven by Russia's invasion of Ukraine.
Insiders at British gas parent company Centrica say this offer is a call to arms for other companies - from all sectors - to do the same at a time of national need.
Sceptics say that it is a token gesture that represents a tiny fraction of the overall cost to households, made possible by having a parent company that is making huge profits on its gas production business which other energy retailers don't have.
Scottish Power have estimated the cost of shielding customers from increasing wholesale energy costs at £100bn. British Gas is saying they are the first to volunteer to put their hand in their own pocket to help struggling customers.
Others say it is a drop in a very deep ocean of looming financial distress.
Customers in fuel poverty and more than £250 in arrears on their energy bills to apply for a grant from British Gas.
A household is considered to be in fuel poverty if it has to spend 10% or more of its income on energy. British Gas told the BBC it would take into account customers' income and household expenditure to determine whether they are eligible.
It said it would continue to donate around 10% of its supply profits every six months "for the duration of the energy crisis, backdated to the start of 2022".
Mr de Leeuw said that Centrica had made a "smart move" which "pre-empts a conversation around a possible windfall tax on the energy providers" and other companies might announce similar measures.
But he said: "This requires billions to fix not millions so we are in the wrong conversation if you want to sort out the energy crisis which is just around the corner."
Centrica boss Chris O'Shea said the support package was worth £25m. "As a responsible business we want to do more to support our customers during this difficult time," he said.
This week rival power company Scottish Power' proposed an industry wide scheme to freeze energy bills for two years.
Boss Keith Anderson said the £100bn plan would see the price cap frozen at the current level, with the government covering the difference between what people pay for energy and how much it costs to supply their homes.
The cost could then be repaid over the next 15 to 20 years and would be underwritten by the UK government.
Mr Anderson said he had submitted the idea to Business Secretary Kwasi Kwarteng who was "seriously considering" it.
So far the government has promised a £15bn package of support for UK households. This includes a £650 one-off payment for eight million low income households and a £400 grant for all homes.
Plans to offer households discounts on electricity bills if they cut use at peak times are also set to be announced by National Grid in the next few weeks.
No 10 previously said there would be no new support offered before a new prime minister is appointed on 5 September.
The current favourite to replace Boris Johnson, Liz Truss, has promised tax cuts and recently hinted at direct financial help for hard-pressed households.
Her rival, Rishi Sunak, has said he would introduce more targeted support for households, and has promised to reduce VAT on domestic energy bills from 5% to zero.
But Resolution Foundation, the think tank, warned that the UK would face a "catastrophe" this winter unless the government stepped in to support the most vulnerable.
It is calling for a 30% bill cut for those on benefits, and for households where all individuals are earning less than £25,000 a year. It also said energy bill freezes, social tariffs and a "solidarity tax" of 1% on all income tax rates would ease the situation.
Meanwhile, the British Chambers of Commerce wants more help for small businesses to cope with rising energy costs.
It wants a grant for businesses and a temporary reversal of National Insurance contributions to "put money back into the pockets of businesses and workers".
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