More than 2.3 million families are living in fuel poverty in England – the equivalent of 10% of households, according to government statistics.

Almost 60,000 households in Birmingham alone cannot afford to heat their homes. The figures from the Department for Business, Energy and Industrial Strategy show the West Midlands city is worst affected, with Leeds, Cornwall, Manchester and Liverpool also in the top five local authorities where households face “eat or heat” choices in winter.

However, rural areas of England are proportionally the worst affected, with more than 20% of households on the Isles of Scilly classified as fuel poor. Other badly affected areas include Eden in Cumbria, Richmondshire and Ryedale in North Yorkshire, and West Devon.

Fuel poverty is calculated by gauging if a household’s income would fall below the official poverty line after spending the actual amount needed to heat the home. The average fuel poverty gap of these households – that is, the amount needed to escape fuel poverty – is £371 a year, the latest figures indicate, with those in privately rented properties hit hardest.

About 20% of households renting from a private landlord are classified as fuel poor and single parents with dependent children are at the highest risk, with almost 25% in fuel poverty.

Clive Lewis, the shadow business secretary, said the figures showed the Tories had to take action to tackle the tariffs of the big six energy companies.

“Under the Tories’ lack of an energy plan, Britain is facing an energy bill crisis, with over 2 million families who can’t afford their energy bills,” said the Labour MP.

“The government must act now on the monopoly of the big six in the energy market and tackle the scandal of fuel poverty. A Labour government will deliver clean energy and curb energy bill rises for households.”

This month, the business department said it would publish an energy supplier league table to instantly show consumers where they could save money on fuel bills. Customers should have the ability to access their energy usage data quickly and easily from their energy companies, the government said, to allow them to use price comparison sites to switch tariffs.

Announcing the measures, the business secretary, Greg Clark, said: “Millions of people across Britain continue to pay too much for their energy. The measures announced are a positive step to help more people benefit from increased choice and competition.

“As the government has made clear, where markets are not working for consumers – in energy or otherwise – we are prepared to act.”