They want the link between Calton Road and East Market Street restored as part of a new masterplan for the station to cope with its expected 66 per cent passenger growth over the next six years.
The walkway would provide a traffic-free and more direct route for cyclists and pedestrians between the top of Leith Walk and the Old Town.
It was opened in the 1890s during the eastern expansion of the station but was shut by British Rail in 1958.
The 200m-long bridge, built into the station’s roof, originally extended over East Market Street to Jeffrey Street.
Its deck was removed as part of the revamp of the roof in 2009, but the higher section of the roof, built to accommodate it, is still visible.
Dave du Feu, of Spokes, the Lothian cycling campaign, said: “We raised this with the city council several years ago, but they didn’t see any immediate or medium-term prospect. However, this masterplan proposal is talking about doubling station capacity, so anything should be possible.”
Jolin Warren, of sustainable transport campaigners Transform Scotland, said: “It would be great to eventually re-establish the link, especially with the new St James development. Done right, this could be the primary route for pedestrians and cyclists.”
John Lauder, national director of cycle route developers Sustrans Scotland, said: “Creating high-quality links connecting existing walking and cycling routes while integrating with public transport are key to success in promoting active travel.”
Stuart Hay, director of walking campaign group Living Streets Scotland, said: “Network Rail should look back to the future in fixing this important walking link between Edinburgh’s Old and New Towns.
“The route should never have been lost, so it’s vital that options for restoring an important direct route across the Waverley valley are fully explored.
“A new walkway would help tackle congestion both within the station and on busy pavements linking historic parts of Edinburgh.”
The scheme also won the backing of former city council leader Donald Anderson.
He said: “This would be great if it could be achieved.
“Recent improvements have made Waverley much better, but that roof – I’d have been happy to see it grassed over, despite the fact it’s listed.
“The link could work really well.”
A spokesman for Network Rail, which owns and runs the station, said: “The masterplan will look at how the station interacts with the surrounding streets.
“The possibility of creating an access over the station could be considered. However, there would need to be a business case for the investment identified as part of that process.”
Transport and Environment Vice Convener, Cllr Karen Doran said: “We would urge everyone to make their views heard on what ideas should be considered as part of the masterplan.”