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James Gillespie's High School currently hosts the secondary-age Gaelic medium education (GME) unit whose pupils are due to get their own school as part of a policy of expanding Gaelic education.
But there is continuing uncertainty over where the new school will be built and now officials have said the project faces a three-year delay.
Gillespie's is already at capacity and will start using the Darroch annexe as overspill, including for the Gaelic pupils, in August 2022.
But current projections suggest, even with the extra accommodation, capacity will be breached again in 2025.
In 2018, research claimed parents wanting to move into the catchment area for James Gillespie's High School faced paying a premium of £173,783 for a house.
Gaelic parents are keen to see a GME secondary but they would like a stand-alone school while the council's preferred option has been a shared campus with a new Liberton High School.
The SNP manifesto at last year's Holyrood elections included a surprise promise of a stand-alone school in a central location.
However, after failing to identify a viable central site or secure funding guarantees from the government, the council was set to launch a statutory consultation in January on the Liberton plan, with a stand-alone school at the old Castlebrae High in Craigmillar as a possible alternative.
But they agreed to parents' requests for further exploration on other alternative sites.
And now education officials say the delay means it is too late to build the Gaelic school and the new Liberton High at the same time and the Gaelic school would have to be built once the new Liberton High is completed, meaning the earliest it could be ready is August 2028.
A report to the education committee said: “Consideration requires to be given to how the pressure on places at James Gillespie can be managed. Options include a catchment review for James Gillespie and/or a placement policy which will ensure GME numbers can be managed within current capacity.”
And an official elaborated: “James Gillespie’s as a school has a rising rolls issue and to deal with that we would look at it as we would in any other school – the things that are possible are a catchment area review, internal reconfiguration, more efficient timetabling of space and extra accommodation.”
The report also said none of the alternative sites looked at – including Lothian Buses’ Annandale Street depot, Fettes police headquarters, the former Royal Victoria Hospital, the council depot at Russell Road, the old Tynecastle High School and the Eye Pavilion – were appropriate.
The committee agreed an all-party motion calling for more details and promised to continue discussions with parents.
Education convener Ian Perry said he had just had a reply to his latest letter to Education Secretary Shirley-Anne Somerville about the new school, which he said still did not give “any clarity”.
He said: “They have a great ability to not say yes or no, but to stand somewhere in the middle. The Scottish Government need to tell us once and for all if they’re going to deliver their manifesto commitment. Until we’ve got that bottomed out I don’t think can move forward. Without that, the parents do not have clarity about the options that are available.”