Only Watford BC has so far decided to recommend a mayor to a referendum (LGC, 9 October), while Hammersmith and Fulham LBC has a mayor elected by the majority group.
The other 11 councils which have made clear their plans to overhaul political structures have opted for a cabinet system.
A survey of 1,000 Lewisham residents revealed 57% were in favour of a directly elected mayor. A council cross-party select committee is taking evidence on which system to recommend to the Labour-dominated local authority in January. Local government minister Hilary Armstrong is to appear as a witness.
'We felt very strongly that some authorities have made decisions without doing too much consultation with citizens. We found people want more visible leadership and their representatives to spend less time in the town hall and more time in the area,' he said.
Middlesbrough BC has opted for a cabinet. Although 46 of the 53 members are Labour, the 10-strong cabinet will include members from minority groups.
Many councils which have moved to a cabinet model have left the power of veto with full council meetings, which is widely seen as a safe, legal option until the government changes existing legislation.
Middlesbrough's plan will see the full council transformed into a Middlesbrough assembly for quarterly meetings which will include input from people from the community, business and the youth parliament.
Managing director John Foster said the changes 'will alter fundamentally the relationship between the council and the people it serves. They will make local government in Middlesbrough more open, effective and accountable'.
This week leaders of the three groups on hung Sefton MBC launched a consultation exercise which proposes an executive board based on proportionate representation of the parties. The full council will continue to approve the budget and key priorities as well as 'any matters which by law only the council can decide'.
Barnsley MBC has also adopted a cabinet system. Nine cabinet members will meet weekly to take 'day-to-day decisions within the budget and policy framework agreed by full council'.