Experts at the national heritage agency said the proposals, which were formally submitted by the Royal High School Preservation Trust in December, represent a “measured reuse of a nationally and internationally important site and building”.

The bid was submitted as an alternative to Hoskins Architects’ £75m plans to turn the school into a hotel, which was narrowly rejected by councillors later that month.

The Scottish Government agency’s opposition to the hotel scheme is believed to have been a key factor in its planning refusal.

Now it has told the City of Edinburgh Council, which owns the building, that it backs its use as the proposed new home for St Mary’s Music School.

Richard Murphy Architects and Simpson & Brown’s vision is for a 300 seat concert hall and the creation of three new public performance spaces and a contemporary foyer providing space for ticketing, bar and cloakrooms that will also double up as a multi-functional space.

In a letter to the local authority, which will decide on the application in the spring, HES stated: “We welcome not only the proposed restoration and repairs to the listed buildings on the site, but also the design of the new school accommodation blocks that, by their scale and positioning, firmly retain the primacy of the Hamilton building on the site.”

Willie Gray Muir, chairman of the trust behind the St Mary’s project, said: “We’re absolutely delighted with the conclusions of Historic Environment Scotland.

“We want our plans to be seen as a solution which fully respects the importance of the building. To get this support at this stage is critical to us.”

A spokesman for Duddingston and the Urbanist Group, the two developers of the hotel project, said an appeal over the council decision was still being considered.