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The 60-bed council-run home will now be given a new function as a complex care assessment unit operated by the NHS.
And another PFI home, Ferryfield House, where complex critical care is provided by the NHS, will also close.
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The Edinburgh Integration Joint Board (IJB), which is in charge of health and social care in the Capital, agreed the moves unanimously.
The closures are part of a wide-ranging review of care provision in the city, which also includes proposals to close four other council-run homes - Clovenstone, Fords Road, Ferrylee and Jewel House. All four have buildings which are said no longer to be suitable.
The board, which brings together NHS and council representatives, was told an early decision was needed on Drumbrae because the change in function was crucial to other elements in the plan which included ending the use of Liberton Hospital, which has been sold for redevelopment.
Last week Unison announced it would ballot members at Drumbrae on possible strike action as part of its campaign to save all the homes.
And Unison assistant branch secretary Gerry Stovin appealed to the board to change its mind.
He said: "We feel the voting members of the board have a gun to their heads: accept this package of cuts and closures or everything will come down around you.
"Residents in Drumbrae have an uncertain future, being taken away from their home, friends and those who care for them.
"For the staff at Drumbrae, faced with the last resort of an industrial action ballot they are unable to vote Yes as it may affect the residents they care for, and unable to ote No as this is a betrayal of the very same people they're there to care for.
"All this for two reasons – a couple of property deals and cuts in bed numbers to save cash."
He argued alternative moves could be made which would keep Drumbrae and Ferryfield open and still allow Liberton Hospital to close.
The board plans to carry out a public consultation based on the remaining parts of the review but has yet to discuss the details of that. Edinburgh’s Labour councillors have already said they will oppose the proposed closures.
But Judith Proctor, chief officer of Edinburgh Health and Social Care Partnership, said: “I don’t think we would be consulting on anything as binary as ‘Are these care homes to close or are these care homes to remain open?’ because we know they have surpassed their design life and it would be difficult to adapt them in a good-value way.
"So I think the result of a consultation – and it would have to be broad and open – would inform the conversations we then have with our partners about the future of care and that would inform decisions that are made by this board and others in relation to the future of those care homes.”