The warning has been issued by the NHS Confederation, the membership body for organisations that provide NHS services.
A decision on the level of the new energy price cap is expected on 26th August, with the latest estimates suggesting that the cap could go as high as £4,200 by January.
NHS leaders predict that if households are not safeguarded from energy price increases, “it will fall to local NHS and social care services to pick up the pieces”.
NHS Confederation Chief Executive Matthew Taylor had previously written to Chancellor Nadhim Zahawi calling on him to announce additional and targeted measures.
Speaking earlier today to BBC Radio 4’s Today programme, Mr Taylor, said: “If demand grows on the health service, then the challenges will also grow.
“It’s absolutely clear that if more people are suffering from fuel poverty, if more people are unable to heat their homes that will drive additional demand.”
A government spokesperson told ELN: “We know that rising prices are affecting how far people’s incomes go, which is why we have taken action to help households with £37 billion worth of support, which includes specific support to help people through the difficult winter ahead.
“Eight million of the most vulnerable households will see £1,200 extra support, provided in instalments across the year, and everyone will receive £400 over the winter to help with energy bills.
“That’s on top of action earlier this year including a record fuel duty cut and a National Insurance cut worth up to £330 a year for the typical employee.
“We are also working closely with the NHS at pace to ensure we are ready for the pressures ahead by increasing capacity, boosting NHS 111 and 999 support, tackling delayed discharge and using new innovations such as virtual wards.”