Campaigners in favour of a directly-elected mayor say their proposal would be cheaper than the alternative committee system.
The No campaign in Brighton and Hove, called Allies for Democracy, has said having a mayor would cost an extra £1 million during four years.
But former council leader Lord Bassam said the committee system would cost at least £2.4 million during that time just so that councillors could talk more.
He said there would have to be 12 extra committees and scrutiny boards which would cost £50,000 per committee and £600,000 a year for new staff.
And Lord Bassam said most of the cost of the elected mayor could be taken from the expense of having a council leader as at present.
Lord Bassam, speaking for the Yes for City Mayor campaign, added: "We feel that the mayor will cost less because of the reduction in the costs of delay and bureaucracy."
Chairman Roger French added: "The costs could be even greater, especially if the proposed community forums (as yet uncosted) are approved.
"The elected mayor will save money, be more efficient in taking decisions and more effective in ensuring that good quality public services are provided."
Meanwhile, Yes campaigners today took their campaign on to the streets.
Fifteen buses carrying 25ft posters displaying the Yes for City Mayor campaign logo are travelling on the city's main routes.
All Yes For City Mayor buses will carry campaign leaflets.
The campaign was launched at 8.30am on a Brighton and Hove open-top bus at Churchill Square. Children sang the campaign theme song Moving On Up from the top deck. Polling is next month.
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