Labour's poor performance in last week's polls means that the Conservatives have taken control of local government's national lobbying organisation for the first time.
Sir Jeremy Beecham, the Newcastle-based Labour councillor, will be replaced by a Tory as chair of the Local Government Association.
The Conservatives will not decide their nomination until the LGA conference in July.
But Sir Sandy Bruce-Lockhart, the current vice chair and Kent county council leader who last year suggested capping pensioners' council taxes, is favourite.
The position of Graham Lane, current Labour chair of the LGA education executive, is also under threat.
Labour's fall to second largest LGA party, with 34.9 per cent of councillors compared to the Conservatives' 35.8 per cent, will give the Tories first choice of committee chairs. And with a reorganisation set to reduce the 19 executives to around eight boards - the education service is expected to be taken into a larger children's services board - there are also fewer to go round.
Mr Lane, leader of Newham council, east London, has been education chair since the LGA's formation in 1997. He was education chair of the Association of Metropolitan Authorities, one of the organisations that preceded it for four years before that.
He lost his position as chair of the teachers' employers' body after eight years in November, when he was replaced by Robert Gordon, Hertfordshire county council's Conservative executive member for education.