Trafford Council’s controlling Labour group has been accused of wanting key decisions to be made "in the dark" after voting down a motion calling for a London-style assembly for Greater Manchester.
The motion, put forward by newly-elected Green Cllr Owain Sutton, was supported by Lib Dems and Conservatives, but defeated by the majority of Labour members.
It comes in the wake of a new devolution deal which will hand over more powers to Greater Manchester Mayor Andy Burnham and the Greater Manchester Combined Authority (GMCA).
The deal agreed in March gives Mr Burnham more control over technical education, housing standards and local trains.
Greater Manchester will also get a single funding settlement which will give the mayor more of a say over how money is spent rather than having to bid for separate pots of cash for specific projects.
In return, Mr Burnham and the 10 council leaders will be subject to scrutiny by MPs as well as local councillors.
But at a council meeting, Cllr Sutton said: “This is about fairness to Greater Manchester and its people.
"No democracy is perfect and it should be reviewed and revised periodically to ensure it remains the best fit for its ever-evolving purpose.”
He said it was time to move away from "opacity" [lack of transparency] of the Greater Manchester Combined Authority (GMCA) to a system "where all voters" voices are represented fairly.
His Green colleague Cllr Hannah Spencer seconded the motion, saying: “If something’s good enough for London, why are we denied it? We’re almost the same size in population as Wales.
“Why did we fight to have an elected mayor if we are denied the accountability that the mayor in London has?”
Supporting the motion Lib Dem, Cllr Shaun Ennis said: “The Greater Manchester Combined Authority has worked to gain powers from London.
“Labour would just prefer to use those powers in the dark in private without too many questions. If an assembly is good enough for London it is good enough for Greater Manchester.”
Conservative group leader Cllr Nathan Evans said: “Never more than now has scrutiny been required within GM.
“When we have seen the GMSF renamed Places for Everyone.
"Whether you support it or not and is rolled on for the best part of eight years and has clearly cost millions with wanton waste of millions of pounds on thousands of unnecessary cameras.
“Even when he [Mr Burnham] attended this chamber, it was a closed meeting. Scrutiny has failed for over six years within Greater Manchester and now reformed allows even less time – 22 hours in a year – to scrutinise £7bn of spend.”
However, Labour Cllr Liz Patel, who is the executive member for economy and regeneration, said she rejected the idea that an elected mayor working with the leadership of elected members is ‘fundamentally undemocratic’.
She said: “The majority of Greater Manchester leaders are of a different political party to the one putting forward this motion is not enough of an argument that it’s unrepresentative.
“GMCA has fought hard for greater devolution of powers from Westminster.
"It’s noted that opposition parties had little to say publicly during that time but waited until that very difficult task is concluding to come forward with the ask for the model to be changed.
“The devolution deal is a hugely complex area of work.
"It will require significant resources locally to work through the implications for us in Trafford.
"As an administration, we are focused on what that means for us in areas such as transport, Net Zero, housing, jobs skills and culture.”
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