But substantial reservations remain over how cutting back on subjects will work in practice.
Earlier this year Education Secretary David Blunkett proposed suspending the detailed national curriculum regime for seven to 11-year-olds so that they could concentrate on maths and English.
In response to a "yes" or "no" Government consultation on the issue, it is understood that the majority of primary schools have answered "yes". Workload has been a longstanding complaint.
But a third of the respondents have also provided detailed comments on the practicalities. It is understood there is concern about disruption caused by any radical changes.
Primary schools are particularly concerned about co-ordinating their work with local secondaries. The National Union of Teachers has called for an extra day's training to help schools plan their curriculum.
David Hart, general secretary of the National Association of Head Teachers, said: "Schools are torn between a clear desire to concentrate on literacy and numeracy and their wish to offer a broad and balanced curriculum. There's a danger that children will be less well equipped for transfer for secondary school."
The NUT has welcomed the slimdown which, if approved, will come into force in September. It will be optional for schools and will last until the review in 2000. "Teachers now have the opportunity for the next two years to demonstrate that the curriculum is theirs and not imposed on them," said the NUT's assistant general secretary, John Bangs.
* The Government has announced it will spend pound;5 million on running 562 summer literacy schools this year. There will also be 30-40 pilot summer numeracy schools.