The survey of 11,000 people in 10 metropolitan areas found 30% of respondents would be more likely to vote in an election for mayor than for individual councillors. But more than half said it would make no difference to the likelihood of them voting.
Two thirds of respondents agreed an elected mayor would make it easier to get things done and make it clear who was responsible when things went wrong.
The greatest concern about directly elected mayors, agreed by 45.5% of respondents, was that the position might give too much power to one person.
People in Middlesbrough - where there has been a high-profile campaign for the post of mayor by suspended police superintendent Ray Mallon - showed the most enthusiasm for directly elected mayors, and Liverpudlians the least.
Only one in four respondents knew about the changes to local government constitutions introduced by Labour, with half claiming they had not had an opportunity to express their views on the reforms.
Critics warn the survey makes too much of the support. Local Government Association Liberal Democrat group leader Chris Clarke said the survey appeared to produce different results to those of the mayoral referendums where the majority had not supported mayors.
He said: 'The government is trying to breathe life into an idea that has essentially fallen on deaf ears.'
A spokesman for the Labour Campaign for Open Local Government said the survey was misleading and cynical: 'The questions are written in such a way as to suggest mayors are all-conquering street wardens and the results reflect that.'
The areas surveyed were Birmingham, Bristol, Derby, Harrow, Liverpool, Middlesbrough, Oxford, Plymouth, Preston and Westminster.
Local government minister Nick Raynsford has told Birmingham City Council he intends to force it to hold a mayoral referendum. The decision was based on the result of a consultation with local people on whether they wanted a mayor or leader and cabinet model.
'We think the council was wrong to maintain the electors of Birmingham had expressed a preference for the leader and cabinet option. A majority expressed support for the two options involving a mayor,' Mr Raynsford said.