The majority of British households expect to restrict their home heating this winter to try to keep rising costs in check, according to research released as the price cap that dictates most bills rose again.

The fuel poverty charity National Energy Action said 58% of households told its survey they were likely to trim their energy use, a nine-percentage-point increase from the level in January.

The proportion of households preparing to ration their heating was even higher among those with chronic health conditions, the poll of 2,443 adults found, rising to 64% for those with asthma and 71% for those with a heart condition.

The cap on how much suppliers can charge for each unit of gas and electricity – set by the energy regulator for Great Britain, Ofgem – rose by 2% from Wednesday to the equivalent of £1,755 for a typical annual dual-fuel bill.

The increase for the October to December period comes despite a 2% fall in the wholesale price in energy markets over the past three months, because money is needed to cover the rising cost of the government’s energy policies.

Experts at the consultancy Cornwall Insight forecast a slight fall in the cap in January, before the cost of supporting new power networks, nuclear projects and other policy costs adds an extra £100 a year to the price cap from April.

Ofgem last week released figures showing the UK’s energy debts have climbed to a new high of £4.4bn and there are a record number of accounts in arrears with no plan to back the unpaid bills.

The regulator is preparing to launch a debt relief scheme alongside the government’s landmark £13.2bn warm homes plan to fix draughty homes and install heat pumps and solar panels.

Adam Scorer, the chief executive of National Energy Action, said: “Unaffordable energy bills present a risk to health – and life – this winter.

“Ofgem’s plans to help people out of debt are welcome but need to go much further. Energy bills are rising, debt levels are rising, fears for the coming winter are rising. The warm homes plan needs to provide this certainty for the long term.”

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Martin McCluskey, the minister for energy consumers, said the government was taking “urgent action to support vulnerable families this winter” by expanding the warm home discount to offer £150 off energy bills to more than 6 million families.

“In the coming weeks, we will be announcing details of the biggest home upgrade programme in British history to improve up to 5m homes, making them cheaper and cleaner to run,” he added.