The north London council, whose school services are being privatised by the Government, was in the middle of its own major shake-up of education when the Liberal Democrats gained control last week.
Under Labour's plans, the council would have become the first in England to a create a trust to replace the borough's education committee.
James Kempton, the Lib-Dem group deputy leader, said: "We won't be going ahead with the trust. The education service must be accountable to parents and to the electorate."
He said he was meeting school standards minister Estelle Morris to discuss concerns that the cost of the privatisation contract is higher than the current education budget.
Cambridge Education Associates's contract to manage the borough's schools, now due to be signed in January for a period of five or seven years, is expected to go ahead.
Islington was condemned by the Office for Standards in Education for failing its children, although it turned out to be the fourth most improved authority in this year's league tables.
Labour, which ruled under the mayor's casting vote since the full elections last year, had controlled the council for more than 28 years with a few months' intermission in 1981 and 1982. The by-election was triggered by the death of a Labour councillor.