Selma Abbey, 32, applied for two places at Hurst Primary School in Bexley Heath for three-year-old twins Leya and Ella in January.
"Unfortunately the volume of these applications can sometimes mean an error occurs."
As their sister Ayla, five, already attends the school - which is about two miles from their family home - she thought it would be plain sailing.
However, a few months later, the mother received two letters; one said that Leya had been accepted, the other informed her that Ella’s application had been unsuccessful because the family’s home is 'too far away' from the school.
The mother-of-three has since been told that, although the council made a mistake, there is nothing that can be done to secure Ella a place.
The girls now face being separated.
A spokesman for Bexley Council said: "We are very sorry for the distress that this mistake has caused. This year we received more than 1,694 nursery applications and 3,078 primary applications.
"Unfortunately the volume of these applications can sometimes mean an error occurs."
Furious mum Selma told the Mail Online: "There’s no appeal system so the only thing I’m clinging on to now is the hope that another family rejects their offer.
"Even though none of this is the school’s fault, they’ll have to clean up this mess. They’ve made calls to the council on my behalf without me even asking them to, and they’ve expressed their outrage which was kind.
"There's no appeal system so the only thing I'm clinging on to now is the hope that another family rejects their offer."
She added: "I’m now wondering if the only way out is to reject Leya’s place and write a late application to a separate school, which I absolutely do not want to do.
"I can’t physically be in two places at once during school run time."
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