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Lib Dem and Conservative councillors have promised to vote with Labour to give it the administration and in return they will get key “non-political” posts.
The three parties together have 34 of the 63 seats on the council, so will be able to block the alternative SNP-Green bid for control.
Nine out of Labour’s 13 councillors will take top posts in the new administration, including three of the new councillors elected just three weeks ago. The Lib Dems are handed three roles, including licensing board chair, and the Tories have two.
Labour group leader Cammy Day, who will become council leader, faced anger from some members of his own group over the deal including the Tories. Sources said some of the councillors felt strongly enough to abstain in the crucial vote.
It had been thought the prospect of an SNP-Green administration would be enough for the Tories to back Labour’s bid for power without any need for jobs to be offered.
However, Councillor Day revealed at a Labour group meeting on Tuesday night that as well as the posts for the Lib Dems he had agreed to give the vice-convenerships of two "non-political" committees to the Conservatives.
One insider said Cllr Day had blamed the Lib Dems for demanding the Tories be included, but the Lib Dems said their support had not in any way depended on posts being given to the Conservatives.
The Labour insider said the group was “extremely divided on this – very angry” and said there was no guarantee all 13 Labour councillors would support the motion for the new administration.
"At no point, at any meeting, up until Tuesday night was there any proposal to give jobs to Tories and in fact at the previous group meeting there was an amendment to the proposal saying there would be no jobs for Tories."
The SNP and Greens both criticised Labour for any deal with the Tories. Edinburgh’s SNP MPs and MSPs wrote to Councillor Day, claiming it would give “credence and justification” to the Tories’ actions following the Partygate scandal at Downing Street.
The letter called a deal with the Conservatives “unthinkable” and said Edinburgh had resoundingly rejected the Conservatives in the May 5 elections, when the party was reduced from 18 seats to nine.
Senior SNP councillor Kate Campbell appealed to Labour to think again. “Instead of forging a right-wing coalition, tenuously bound together along constitutional lines and with dubious legitimacy, Labour could join us. An SNP-Labour-Green coalition could deliver progressive, left-wing policies and build a brighter future for our city.”
And Edinburgh Green co-convener Claire Miller said Labour looked set on betraying the people who voted for them. “The majority of voters backed strong council action on poverty, on the climate emergency and inclusion. It's not too late for councillors of all parties to back that option by supporting the clear vision and commitments in the Green and SNP proposal.”