Cammy Day, the council’s Labour deputy leader, who is in a ruling coalition with the SNP, confirmed the past commitment to a workplace parking levy would not be included in his party’s manifesto for the local elections in May.
Lesley Macinnes, the council's SNP transport convener, decried the move as an “enormous pity”.
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The council had said it would consult over plans for a levy once the power to introduce such schemes was handed to local authorities by the Scottish Government next month.
It would see employers be charged for workplace parking spaces – in Nottingham the annual levy is £428 per space or around £2 per working day – which could be passed on to staff.
Former Labour council leader Mark Lazarowicz tweeted: “I was disappointed to hear last night from @cllrcammyday that @EdinburghLabour local election manifesto would drop long-standing commitment to workplace parking levy in Edinburgh.
"Presumably as a result of pressure to follow @ScottishLabour policy on this. A very retrograde step.
“Totally wrong for @scottishlab to determine policy for local elections in this way. We criticise others for centralising policy. So is this.”
But Edinburgh Labour councillor Scott Arthur tweeted: “The group's position is unchanged from 2017, but if the manifesto changes that we will accept the update. We are a democratic party.”
Ms Macinnes said: “It’s an enormous pity that Edinburgh Labour have accepted this directive from Scottish Labour, despite their previous strong support for the exploration of a levy, and that Labour have led the way in introducing this in some English local authorities.
“This is a policy which can help to reduce air pollution and support sustainable transport in Edinburgh as any revenue raised would provide funding for major improvements."