Shadow business secretary Clive Lewis said action was needed following figures showing that one in 10 households can't afford to heat their homes.
More than 2.3m families – equivalent to 10% of households – are living in fuel poverty in England, according to official figures, with rural areas proportionally the worst affected.
Households are deemed to be in fuel poverty if their income would fall below the official poverty line after spending the amount needed to heat the home.
More than 20% of households on the Isles of Scilly are classified as fuel poor.
Other badly affected rural areas include Eden in Cumbria, Richmondshire and Ryedale in North Yorkshire, and West Devon.
On average, affected households would need an extra £371 per year to escape fuel poverty, according to figures quoted by The Guardian website.
Mr Lewis said: "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."
The government announced last month that it would publish an energy supplier league table to show consumers how to save money on fuel bills.
It said households should be able to access their energy usage data quickly and easily – enabling them to use price comparison sites to switch tariffs or energy suppliers.
Business secretary Greg Clark said mMillions of people across Britain were continuing to pay too much for their energy.
"The measures announced are a positive step to help more people benefit from increased choice and competition," he added.
"As the government has made clear, where markets are not working for consumers – in energy or otherwise – we are prepared to act."
Sign up to our newsletter to receive all the latest news and updates.