Nearly one in 10 parents are “very likely” to use a food bank to feed their children over the next three months, a survey has found.

It means that as many as 1.3 million parents are expecting to have to visit a food bank as families struggle to cope with rising costs of living, with 88% of those surveyed admitting their monthly food bill has increased in the past three months alone.

The Trussell Trust research, carried out with the food delivery company Deliveroo, also found that a third of parents skipped at least one meal to keep up with other costs, while 20% said they had been unable to cook hot food at least once in the past three months because of the cost of using an oven.

Of those who said their household bills had gone up, 58% said they had cut back on heating as a result.

Emma Revie, the chief executive of food bank charity, said: “Everyone should be able to afford their own food, but as families face the biggest income squeeze in a generation, people are telling us they’re having to make impossible decisions between heating and eating and being forced to turn to food banks to feed themselves.”

She said the charity was about to enter a partnership with Deliveroo to provide up to 2 million meals and support for people facing hunger across the country.

“Our new partnership with Deliveroo will help us support food banks to provide emergency food and in-food-bank support to thousands of people in immediate crisis while we work towards our long-term vision of a future where nobody needs to turn to charity to get by,” she said.

Will Shu, Deliveroo’s chief executive, said: “I am pleased we are partnering with the Trussell Trust to support local food banks across the country. We’re committed to using our platform to play a positive role in the communities in which we operate.

“Together with our consumers, our amazing restaurant and grocery partners and our network of riders, we want to play our part in helping to tackle food insecurity in the UK.”

The archbishop of Canterbury spoke in his Easter Sunday sermon at Canterbury Cathedral of his concern for families struggling with rising energy and food prices.

“Families across the country are waking up to cold homes and empty stomachs as we face the greatest cost-of-living crisis we have known in our lifetimes. And because of this they wake up with fear,” he said.

Leading analysts warned last week that energy bills would stay well above £2,000 for two more years.

Cornwall Insights, which approximately predicted the recent 54% rise in the cap on average energy bills to £1,971, said that prolonged high prices would threaten the chancellor’s loan scheme to help households cope with the soaring cost of gas.