The once-influential Socialist Educational Association, which is affiliated to the party, is riven with dissent between Old and New Labour and about to split.
Its national executive last month voted to accept Labour's education policy and plans, but many of its branches want to stress the SEA's independence. The turmoil places ministers and MPs who are members in an embarrassing position.
Members of the SEA in Parliament include Gordon Brown, Margaret Beckett, the President of the Board of Trade, and the education team. Stephen Byers, the schools standards minister, is one of its vice presidents, and Margaret Hodge, chair of the Commons education and employment select committee, has recently joined.
Labour Euro MP Robert Evans and Pauline Green, leader of the Socialist Group in Europe, are members. So, too, are former Labour leader Neil Kinnock, the European Commissioner for transport and his MEP wife, Glenys. Tony Blair has never joined.
At the heart of the dispute is the future role of the SEA. Should it be part of the party's policy-making or independent? Meetings have been held with education ministers and more are to take place with party officials shortly.
Graham Lane, the education chair of the Local Government Association and SEA general secretary, has threatened to resign. He believes the SEA cannot be semi-detached from the party.
And earlier this month almost all officers of the SEA were persuaded not to resign either from the national executive or the association. There have been disputes between several members of the national executive and the chair, Max Morris, a past president of the National Union of Teachers.
Once called the Association of Labour Teachers, the SEA was set up to develop policy and give education a higher profile within the party.
Earlier this summer the SEA told the Government it was preparing to be a "critical friend" and now plans a New Year relaunch with the SEA playing a "full and enthusiastic" part in the Labour party and its educational policy.