The Trussell Trust, which is a Christian charity that runs a network of food banks across the UK, distributed 87,496 food parcels for children during July and August 2018, up from 73,226 the previous year.
The charity urged the public to donate food, warning that summer holidays can mean children missing out on school meals, and the extra cost of childcare can cause difficulties for hard-pressed families.
Food bank use overall increased by 19 per cent in 2018-19 according to the Trussell Trust's figures, and the charity expects the trend to continue.
The trust's chief executive Emma Revie said: "Food banks will do all they can to help families over the summer, with many running holiday clubs to support parents who find that their income simply won't stretch to meet the extra pressure of missing free school meals or paying for additional childcare during the holidays.
"But no charity can replace the dignity of having enough money for the basics."
She called on the Government to ensure that benefit payments cover the "true cost of living" and that work pays a "real living wage".
"Every family should have enough money coming in for a decent standard of living," she said.
"No child should face going hungry in the UK."
The Trussell Trust said that tackling delays and gaps in benefits should be treated as a priority by the Government.
It called for an end to the five-week wait for a first Universal Credit payment, which it claimed was a key driver of need at food banks in the charity's network.
Shadow work and pensions secretary Margaret Greenwood said: "The Government cannot simply abdicate responsibility for families being pushed into poverty and children going hungry in the summer.
"Labour will stop the roll-out of Universal Credit and make tackling child poverty a key priority for Government once again."
Government officials said 95 per cent of UC claimants are paid in full and on time, with advances available for people who cannot wait for their first payment.
A Government spokesman said: "Our priority is to support people to improve their lives through work while helping low income families with the cost of living.
"That's why we have raised the personal allowance to take 1.74 million of the lowest paid out of income tax altogether, frozen fuel duty for the ninth consecutive year, increased the National Living Wage and confirmed that the benefit freeze will end next year.
"Meanwhile, we've seen record high employment and wages continuing to outstrip inflation so people have more money in their pocket."
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