The Education Authority (EA) has published a plan to close Ballougry Primary School in August 2023.
The EA said the 44-pupil rural school which is three miles from Derry was unsustainable.
The Silent Witness star, whose dad was a former headmaster, described the school as “magical”.
She was a pupil at the school between 1961-17 and her father retired in 1979 from his post as school principal after 32 years service.
Speaking to BBC Radio Foyle, Ms Burton said: “I traipsed through the school garden every day to be taught.
“I had to leave when I went into the city to further my education, but it has such a special place in my heart but obviously that’s not a reason to keep a school going.
“For me, in the first instance, it was such a magical place for me to grow up in – the surroundings and the education that can come with a smaller school, a personal and intense education that you can have with smaller class groups, I am a great advocate for that.”
The EA is responsible for planning the future of schools in the North of Ireland.
Some children travel three miles from Derry to attend Ballougry Primary and it also has six pupils from Co Donegal.
The EA said that with only 44 pupils and three teachers, the school is well below the Department of Education’s (DE) recommended number of 105 pupils for a rural primary school.
The controlled school’s financial deficit was likely to rise to about £250,000 by 2024, it added.
Ms Burton said she would be “first in the queue” to enrol her children at the school if she was based nearby.
“For me it just fuelled my imagination, and ultimately that had a big leaning to me to go on and be an actress,” she added.
The EA’s plan to close the school stated that pupils from Ballougry could attend primaries in Derry instead, where they would have more educational and extra-curricular activities.
Ms Burton said: “The school is a very progressive one, it is integrated, takes pupils from both sides of the border, it has a lot to give.
“I believe it needs time to grow post-pandemic, if we can cross our fingers and say that’s the space we are in now, in that the school can have a school life again for children in normal time, with a very committed headmaster and PTA (parent teacher association).”The actress, who also played a principal in the BBC drama Waterloo Road, recounted her rural upbringing.
“I definitely had the space to grow as a child there, without a doubt it fuelled my ambitions to be an actress, and also I think gave me the most deep-seated love of the countryside, a real lasting impact on me,” Ms Burton said.
The EA has launched an eight-week consultation on their proposal to close the school.
However, a future education minister will ultimately decide whether it shuts its doors with a final decision expected in January 2023.
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