Officials in the Treasury reportedly want family doctors to assess whether sick or elderly people need a discount heating their homes.
The idea, reported in the Sun on Sunday newspaper, is said to be one of a number being discussed in government to help with the cost of living.
But shadow health secretary Wes Streeting warned the plan would simply put more pressure on the NHS over the winter.
"The Conservatives have lost the plot on the cost of living crisis and haven’t got a clue about the level of pressure on the NHS," he said.
Mr Streeting said Labour "already has the right prescription for dealing with rising energy bills". The opposition says it would pay energy companies to freeze the energy price cap where it is.
This would head off expected increases to over £3,000 over the winter.
The Liberal Democrats have come forward with a similar proposal, while the Green Party says prices are already too high and should be cut to last year's levels.
Treasury officials apparently believe using GPs to target energy bill discounts will save money because it will help target cash at people who need it most.
On Sunday afternoon the British Medical Association (BMA) said they “completely reject” the policy and branded the government's approach to policymaking “deeply unprofessional”.
Dr David Wrigley, BMA England's GP committee deputy chair, said: “At a time when GPs are already overwhelmed with the greatest workforce crisis and longest waiting lists in memory, this addition to their workload is totally unacceptable.
“It beggars belief that government ministers think it is appropriate to suggest GPs undertake this work.”
He added that GPs “do not have the time or the skills to do the work of the welfare system”.
“In these next few months GPs already have to worry about delivering the Covid and flu vaccination programmes that will be necessary to see the NHS through the winter, on top of their daily crushing workload and the enormous Covid backlog we now see,” he added.
“The government has not discussed this with us in any form - floating these sorts of proposals via the media is deeply unprofessional. We completely reject any suggestion that GPs do this work."
The government has offered little in the way of concrete policies on cost of living since the spring, with the Conservatives focusing on a party leadership contest.
New proposals are expected from whoever wins the contest next month, with an emergency budget expected in the autumn.
The Times newspaper meanwhile reports that the National Grid is taking action and planning to reward customers for shifting power-hungry activities to low-demand times.
It will ask regulator Ofgem to let it pay customers to shift tumble-drying and dish-washing to overnight. The grid operator hopes the scheme will be in place by October if approved.
The latest forecast for the energy bill price cap warns that bills could soar as high as £6,000 by April.
Consultancy Auxilione says that the cap is expected to reach £3,576 in October, rising to £4,799 in January, and eventually hitting £6,089 in April.
Until April this year the cap was just £1,277, but prices have been pushed up by the war in Ukraine and a surge in demand caused by the reopening of economies after Covid-19 lockdowns.
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