The Labour Party claims a full roll-out of Universal Credit will take the meals away from children on the benefits system, as it says families will become ineligible for them.
The latest Department for Education survey on school populations in England found that 18% of state school pupils in Doncaster received free meals at school lunchtimes in January – 8,510 children in total.
This is higher than the rate across the country, at 15%.
Since 2018, the proportion of pupils claiming the meals in Doncaster has risen by 2.6 percentage points.
Children in Reception, Year 1 and Year 2 are automatically offered free school meals, but from Year 3 eligibility is linked to parents' benefits.
In Doncaster, 18% of primary school pupils claimed free school lunches .
In secondary schools, 17% had them.
Nationally, the number of children receiving free school meals in England is at its highest level since 2014.
Angela Rayner, Labour’s Shadow Education Secretary, said: "The Government's short-term solution for the failings of Universal Credit has a brutal expiry date: if UC is ever rolled out, the Tories will stop the children of families on UC being automatically eligible for free school meals.
"The Tories and, in coalition, the Lib Dems, have refused to provide disadvantaged children with the best start in life, with years of cuts to social security leading to rising child poverty.
"The next Labour government will give every primary school child a free school meal, and invest in schools, children’s services and the social safety net – so we can guarantee every child the best start in life."
The Department for Education dismissed the Labour claims as "scaremongering", adding that pupils eligible for the meals on or after 1 April last year can still claim them even if their circumstances change.
They say fewer youngsters stopped being eligible for them as a result.
A spokeswoman added: "Thanks to the protections included in our new free school meals criteria, the proportion of pupils eligible for and claiming these meals has risen across all ages this year which is fantastic to see.
"Contrary to previous scaremongering that disadvantaged children will lose their free school meal, data published just last week shows that more children are eligible for and claiming a free nutritious daily meal.
"We encourage all schools to speak to parents and pupils about their school meals provision, to ensure as many eligible children as possible claim their free school meals."