TEACHERS and parents have hit out at council cuts to education services, warning the "very heart" of the school system is under threat.

The stark warning comes as the latest local authority to announce its budget proposals has targeted £6 million of cuts at education service.

Under the plans published by Falkirk Council, teacher numbers and support staff could be cut as well as the number of subjects on offer, as officials try to make £40m of savings over the next three years.

The council is also considering axing the school library service in primary schools and doing away with breakfast clubs.

A number of other councils have come forward with plans to cut education services. South Lanarkshire suggested class sizes in deprived communities would be increased and teachers axed. Other options include cutting the number of qualified nursery teachers. East Renfrewshire said it was considering having larger English and maths classes.

Last night, parents and teachers' representatives warned the quality of Scottish education would inevitably suffer.

Ken Cunningham, general secretary of School Leaders' ­Scotland, which represents secondary headteachers, said: "This is confirming our worst fears of where councils are heading in terms of finance and the lack of protection for education.

"We have already warned about inequality in schools across the country, but it is now hitting right at the heart of the delivery of education, especially with the reduction in staffing.

"Teachers are right in the middle of delivering new qualifications, and any reduction in staff will influence that."

Eileen Prior, executive director of the Scottish Parent Teacher Council (SPTC), said it was ­inevitable that continuing cuts would begin to hit schools hard, and instead called for greater efficiencies in the way education services are run.

She said: "There are already cuts within the school service and this is just the next stage of cutting much deeper, and our perspective is that we have to stop and think whether the way we run education needs to be looked at.

"There is a lot of duplication between the 32 local authorities, and rather than cutting what is going on in school we need to look at whether we can save money by making efficiencies in the way schools are run."

Larry Flanagan, general ­secretary of the Educational ­Institute of Scotland called for a new agreement with councils to project teacher numbers.

A spokesman for council umbrella group Cosla said ­education was the largest local government service, costing councils £5 billion a year. He said: "Local authorities are legally required to deliver a balanced budget, which means they have to take into account financial pressures.

"It's no surprise the biggest financial challenge facing authorities on education is balancing the requirement for maintaining staff and school building with other service demands. Councils will try to engage the public as best as possible on the future of education services, but the reality is that all councils face difficult and potentially unpopular decisions."

Craig Martin, leader of Falkirk Council, added: "The reality is there is no meat left on the bone. The further £40m of cuts over the next three years are going to hurt, and now vulnerable people will feel these cuts bite."