The leadership of Bromley's Conservative group has changed twice in the past year, with Michael Tickner having been ousted in May 2003 and Russell Mellor last month.
The LGA hoped that new leader Stephen Carr, who won in a four-way leadership fight, would be more sympathetic to membership of the body.
But he said: 'My first reaction is 'no'. The administration felt that we did not get enough out of the LGA.
The complex arithmetic of the LGA's political weighting system could see the Tories take the top posts if they have done well in the local elections, with Kent CC leader Sir Sandy Bruce-Lockhart expected to replace Labour's Sir Jeremy Beecham as chair.