And over a quarter are staying in places suffering from damp or mould.
The Children's Society study, based on a poll of around 2,000 10-17-year-olds, reveals the stark conditions faced by youngsters living in poverty in the UK.
Of those who said that their families are "not well off at all", around 53% said that they do not have enough space, while a similar proportion admitted that their homes were much, or a bit, colder than they would have liked last winter.
Just over one in four (26%) said that their home was damp or mouldy.
The poll, published to mark the launch of the first Children's Commission on Poverty, also reveals that many youngsters believe the situation is worsening.
Around three quarters of those questioned said that they worry about how much money their family has, while nearly half (49%) said that child poverty has increased in the last decade.
Around four in 10 (41%) said they think this will increase in the next 10 years.
The Children's Society, which said that figures show over three million youngsters are currently living in poverty, said that the findings are a "wake up call".
More than half of those surveyed who said that their families are not well off at all revealed that they had felt embarrassed, while one in seven (14%) admitted they suffered some type of bullying.
The Children's Society said that the new Commission - led by a panel of 15 children and young people from across England - will conduct an 18-month inquiry into child poverty in the UK.
The charity's chief executive Matthew Reed said: "For millions of children up and down the country, poverty is a grinding reality - and it is getting worse. Many families are facing stark and unacceptable choices, like heat or eat. This is disgraceful in any country - especially in one of the world's richest. Yet their voices are being left out of the debate. That is about to change.
"The launch of the Children's Commission marks a major milestone in the debate around child poverty in this country. For the first time it is being driven by children themselves, who will show us, through their own eyes, what it looks and feels like to be in poverty."
A spokesman for the Department for Work and Pensions said: "Despite paying out £170 billion in tax credits alone, the previous government failed to meet their target to halve child poverty by 2010 and far too many children were left behind.
"While this Government is committed to eradicating child poverty, we are taking a new approach by finding the root causes of the problem and tackling these. We have successfully protected the poorest from falling behind and last year we saw a reduction of 100,000 children in workless poor families.
"Our welfare reform programme and tax changes will further increase work incentives and improve the lives of some of the poorest families in our communities. The introduction of the Universal Credit will make three million households better off and lift up to 250,000 children out of poverty."