Citizens Advice said as many as 140,000 households are going without power, as they cannot afford to top up their prepayment meters.
And the Living Wage Foundation - which campaigns for fair pay - said many of the poorest parents are skipping meals.
The survey conducted by Citizens Advice suggests that most households which cannot afford to put money in the meter contain either children or someone with a long-term health condition. Some people are left in cold houses, or without hot water.
"It is unacceptable that so many vulnerable households are being left without heat and light," said Gillian Guy, the chief executive of Citizens Advice.
A separate survey for the Living Wage Foundation suggests a third of working parents on low incomes have regularly gone without meals, because of a lack of money. Around a half of those families have also fallen behind with household bills.
"These findings reveal the desperate choices low paid families have to make, and show why it's so important that more employers take a stand by paying the real Living Wage, based on what they need to live, not just the government minimum," said Tess Lanning, director of the Living Wage Foundation.