The Institute for Government has called for directly elected mayors to be given more powers.
Institute director, Lord Adonis, has written to communities secretary Eric Pickles, and called on the Government to give mayors more powers over planning and policing.
The former Labour minister also called on the Government to spread the planned referenda on mayors in 11 English cities over two years, instead of holding them all at the same time.
Lord Adonis said Birmingham, Leeds and Bristol should all be able to vote first on directly elected mayors in May 2012.
'Staging the referenda over the next two years would give an opportunity for those voting in the second wave to see the mayoral model working in the first,' said Lord Adonis.
'If these cities vote in favour of mayoral elections, these should then take place earlier than planned in September 2012. This would avoid a period of possible hiatus between yes votes and elections, whilst allowing enough time for candidate selection and campaigning.'
The Institute has also published a new report , entitled Making the Most of Mayors, which recommends that they should have the power of veto over the appointment of chief executives.
It also calls for a review of the number of councillors in local authorities with a directly elected mayor.