The consultation gave an ambiguous result, with 46% in favour of cabinet and leader (option one), 40% in favour of mayor and cabinet, and 13% in favour of mayor and council manager. The turnout was 31%.
This represents a victory for a cabinet and leader if the other options are taken separately, but for a mayor if they are lumped together. However, in either case the margin of victory is slim.
While council leader Albert Bore (Lab) is pro-mayor, there are divisions within the Labour group, and the Conservatives are largely anti-mayor.
Deputy Conservative group leader Mike Whitby said: 'The citizens of Birmingham have expressed their desire for option one. Any tampering with that will debase the rules of local democracy.'
Network director John Williams said: 'The council is duty bound to hold a binding referendum. If they don't, central government should intervene in accordance with the wishes of local people.
'We trust local politicians will see the light, 88 (out of 117) of them were elected on lower turnouts than this consultation. If this was a referendum it would have produced an overwhelming yes vote.'
Local government secretary Stephen Byers is considering forcing Southwark LBC to hold a referendum. It submitted a cabinet and leader model to the DTLR despite majorities of up to 75% for a mayoral model in consultations. Mr Bore was unavailable for comment.