Under the plans, East Lothian Council could become the first in Scotland to create an arms-length trust to run its schools.

Part of a wider budget review by the council – jointly run by the SNP and Scottish Liberal Democrats – the plan could result in schools devoting more time to specialist subjects and even seeking financial support from the private sector.

The Educational Institute of Scotland, the country’s largest teaching union, attacked the plan.

“While the proposal currently appears to be highly speculative and lacking in meaningful support, the EIS would have serious concerns about any potential return to the failed opt-out type policies of the past,” said a spokesman.

“It is already difficult to recruit headteachers in schools, without adding yet another responsibility to the job and removing the established local authority support.

“At a time when many schools are already suffering as a result of financial cuts, asking headteachers to take on additional financial responsibility over diminishing budgets would only add to the pressures upon them.”

However, Ken Cunningham, general secretary of School Leaders Scotland, which represents secondary heads, said the idea was worth exploring.

“The world in which we now inhabit in terms of finance means that we have got to get a bit more imaginative about how we manage schools,” he said.

“The more autonomy a school has within its local community the easier it is for headteachers, along with their colleagues in school and parents, to take local decisions based on local needs.”

The comments came after East Lothian Council included proposals for educational trusts in a 2012-13 budget document titled You Pay, Have Your Say: Spending Choices.

The section of the East Lothian document on trust schools says: “There may be benefits in establishing educational trusts to deliver education on behalf of local communities. Such trusts may access additional funding from other sources and may also benefit from not having to pay rates.”

Although the idea is not supported by the SNP Government at Holyrood, David Berry, East Lothian Council’s Nationalist leader, said he hoped the plan would lead to a national debate on new ways of giving schools greater freedom over their finances.

Trust schools, which are supported by the Labour Government at Westminster, have proved popular in England, with hundreds of schools already taking up the status.

South of the Border, such schools are funded by councils but run by governing bodies that can employ their own staff, make separate admissions arrangements and manage their own assets. Governors of trust schools can include representatives from private business.

Mr Berry said: “The idea is to look at school clusters – high schools and their associated primaries – to form trusts, and give them more freedom to spend money as they see fit to serve their communities.”

Mr Berry said it was very difficult for schools to be flexible currently because of the way budgets were allocated.

He said more flexibility could allow, for example, a school to reduce subsidised bus travel for pupils and use the money instead to bring in a specialist Mandarin teacher.

He also suggested a school with a strong sporting background might want to spend more on buses to rugby matches – while another might decide to spend more on arts and crafts materials.

The proposals were immediately condemned by the Labour Party in Scotland, but have been backed by the Conservatives.

A Scottish Government spokesperson said: “Any decision over the funding and management of an individual state school would be a matter for the relevant local authority. Ministers have not been approached on the issue of trust schools.”