The new unitary Brighton Council is experimenting with cabinet style leadership. Leader Steve Bassam said an elected mayor would 'create a political structure that cuts through a lot of the unnecessary bureaucracy.'
This structure would speed up development programmes and help bring in private investment, he told Today.
Former Manchester City Council leader Graham Stringer said an elected mayor would have helped the city in its bids for international events.
But John Harman, former leader of Kirklees MBC feared such a system would weaken accountability.
'It would set up two different mandates locally,' he said, and could lead to stand-offs between the leader or mayor and the rest of the administration.'