Headteachers have warned that schools across Scotland face severe cuts as a result of new funding arrangements set up by the Scottish Government and local authorities.

Secondaries are facing a raft of cuts which could see subject choices reduced, larger class sizes and fewer support staff to help vulnerable pupils, the Headteachers' Association of Scotland (HAS) said yesterday.

Its warning was one of the starkest yet of the implications of the historic concordat between central and local government signed after the SNP came to power. Other critics of the new deal have included charities covering the voluntary sector, carers, and environmental groups.

The government has given councils an extra £70m to deliver its manifesto pledge to freeze council tax, but also asked them to deliver savings of 2%.

In addition, the concordat gave more power to councils to take decisions about how they spend public money by ending the practice of ring-fencing where money has to be used for a specific service such as education.

The intention was to enhance local democracy, but there are fears some services, which previously had protected budgets, could lose out because of changing priorities or a shortage of money.

Bill McGregor, general secretary of the HAS, said heads across Scotland were now having to make budget cuts, which in the case of an average secondary school amounted to £70,000.

He said: "We have concerns that the impact of the concordat and efficiency savings on schools could be very serious. Schools are being told they have to make cuts and the scale of these means that we now have huge concern over cuts to courses such as Advanced Higher because the staffing is not there."

He added: "We also cannot see how it will be possible to reduce class sizes and we may even see classes increasing in some areas."

Greg Dempster, general secretary of the Association of Headteachers and Deputes in Scotland, which represents primary headteachers, added: "What we are hearing from members is that headteachers are expecting to have standstill budgets at best - which in effect means a cut - or are seeing real cuts."

A spokesman for the Educational Institute of Scotland, the largest teaching union, added: "While we are yet to see a full national picture, it is clear that an increasing number of local authorities are seeking to make significant cuts in their education budgets."

Both Cosla, which represents local authorities, and the Scottish Government yesterday denied the headteachers' accusations, saying there was no need to cut frontline services.

Cosla attacked the HAS position as "inaccurate". A spokeswoman said: "It is deliberately misleading to say that efficiency savings equate to cuts in frontline services.

"Efficiency savings are exactly that - savings delivered from the efficient operation of services.

"They are intended to free up money for frontline services, like education. Indeed for the first time ever local authorities have the ability to re-invest any savings made to help local communities prosper.

"Councils have to make difficult decisions every day about service delivery but it is completely wrong to suggest that education is being penalised or that local authorities treat education provision as anything less than the highest priority."

A Scottish Government spokeswoman said MSPs had provided record funding across the board for authorities, with an extra £34.9bn over the next three years, with the addition of being able to reinvest efficiency savings.

And, under the concordat, she said there were specific arrangements to maintain teacher numbers and reduce class sizes.