Schools from the two sectors are being encouraged to forge closer links so that pupils can study for Advanced Highers at each other’s schools.

Although Advanced Highers are considered Scotland’s most prestigious exam, provision is patchy because they are expensive to run and some schools don’t have enough staff to teach all subjects.

However, a recent survey by the Scottish Council of Independent Schools (SCIS) found the range of provision much more widespread when qualifications offered by both private and state schools were considered.

Some private and state schools -- such as Glasgow Academy and Hillhead High in Glasgow and George Heriot’s and St Thomas Aquinas in Edinburgh -- already operate similar informal arrangements.

But if the suggestion is adopted more widely it would mark a historic collaboration between the two sectors, traditionally wary of each other.

Private schools believe the high quality of education they offer is of enormous benefit to society, but are seen in some quarters as elitist because entry for most is restricted to families who can afford the fees.

The move could also help private schools retain charitable status because offering free qualifications to state school pupils would represent a clear public benefit -- a requirement under new laws.

Judith Sischy, director of SCIS, said: “The Advanced Higher is arguably one of our best qualifications and can make a key contribution to Scotland’s economic well-being.

“We believe it should be widely accessible, nurtured and promoted wherever possible, but statistics show that, although Advanced Highers are offered in a wide range of subjects, a significant proportion are taught in small groups.

“We would like to see greater sharing of resources, particularly where there are shortages in subject specialists.”

Ms Sischy said the objective of the proposal was to improve opportunities for Scotland’s young people “no matter which school they attend”.

“Reciprocal arrangements are a win-win for pupils and would also bolster take-up of Advanced Higher. In a climate of financial cuts and economic pressures, it seems wise to explore all opportunities for sharing of resources,” she added.

Last night, local authorities welcomed the suggestion and said it could form the basis of wider collaboration between the two sectors.

Steven Purcell, leader of Glasgow City Council, said: “This builds on the good personal and professional relationships between independent schools and the council.

“I welcome the discussions that are taking place and I am sure that a closer working partnership will benefit all Glasgow’s citizens.

“Staff and schools in the city have a wealth of experiences and good practices that can be shared for mutual benefit and understanding.”

Alistair Hector, headmaster of George Heriot’s, said a number of pupils from Edinburgh state schools, including St Thomas Aquinas and Boroughmuir High, have studied Advanced Highers with them over the past few years. The school has also sent pupils to study at St Thomas Aquinas in the past.

“If we have space in the Advanced Higher classes, then we are very pleased to offer places for free to pupils from other schools,” he said.

“It is an informal arrangement, but it works very well for pupils who would otherwise not get a chance to study the subjects of their choice.

“There is also a wider benefit which stems from the collaboration between the pupils and we see this as a very healthy development.”

Advanced Highers were established to give the brightest pupils in Scots schools a qualification in their final year which would prepare them for the rigours of university life and is seen as superior to A-levels by leading UK universities including Oxford and Cambridge.

However, the qualification is also seen as expensive to run by schools because it requires a teacher to give up several hours a week to teach just a handful of the brightest pupils.