A trade union leader has said the bitter row with the SNP Government over a pay rise for teachers could lead to schools closing early.

Larry Flanagan, the general secretary of the Educational Institute of Scotland (EIS), made the claim after SNP Cabinet Secretary John Swinney and local authorities bypassed the unions and wrote to teachers directly about their pay offer.

In a leaked email, Mr Flanagan said if councils wanted teachers to read the joint letter then the school day may have to be cut short, as such a meeting would not be covered by working time agreements.

He also wrote that teachers could defy Mr Swinney by organising a “return to sender” campaign or by protesting to him directly.

Tory MSP Elizabeth Smith criticised the prospect of schools closing early: “Many parents will be very concerned about these revelations especially those which imply teachers are being told schools could close early in order to address the issues raised by the EIS.

“No-one doubts there are significant pressures in the teaching profession just now but this is not the way to go about resolving them.”

However, Mr Flanagan told the Herald on Sunday: “We're not advocating early closure, clearly, just highlighting the practical difficulties of heads being told to call meetings.”

Pay for teachers is determined by a tripartite body which includes the Government, unions and the local authorities, but no agreement has been reached for this year.

The unions want every teacher, from probationers to heads, to receive a 10% rise, while Mr Swinney and COSLA, which represents councils, have tabled a 3% offer.

However, the COSLA/Swinney proposal also includes a rejig of the main grade scale which would put more money into the pockets of teachers. Defenders of the offer say it would give some teachers a rise of over 10%.

The EIS has urged its members to reject the plan in an advisory ballot on the proposal, which could be followed by a statutory strike vote.

Relations between both sides were antagonised after Mr Swinney and Tory councillor Gail Macgregor, who is COSLA’s resources spokesperson, contacted teachers in a joint letter.

They wrote: “We firmly believe that this is a fair offer which demonstrates that both Local Government and the Scottish Government value the teaching profession. We are disappointed that it has been rejected by the teacher unions.

“The teacher unions’ claim for 10% in a single year cannot be achieved. It is simply unaffordable, and the unions have been told this since their claim was submitted at the start of the year.”

They continued: “In the case of teachers, we are looking to invest a total of £105m into the annual pay award and the restructuring of the main grade, the combined impact of which would mean that most teachers would see their pay increase by between between 5% and 11% over the course of 2018-19, when incremental progression is factored in.”

The unions were furious about the letter as they believed it amounted to an interference in their internal democratic practices.

In an email to EIS colleagues on Friday, Mr Flanagan outlined a suite of options that teachers could adopt when responding to the letter.

This included a “letter of protest” to a council leader if a local authority pushed ahead with sending the communication, or emails to councillors, local MSPs, Mr Swinney and Mrs Macgregor.

He also suggested a “return to sender" campaign as well as directing teachers to the EIS website for the “actual” facts.

However, he also advised members of what they could do in circumstances where teachers are asked to attend a school meeting at which the joint letter would be distributed.

Mr Flanagan said union reps should be advised to protest to the headteacher and contact their local EIS association.

In cases where heads are union members, the general secretary said they should protest to the council and “perhaps ask if an early closure is envisaged, as the school WTA [working time agreement] doesn’t have a meeting scheduled”.

A WTA is a collective agreement reached at school level between the trade unions and a headteacher. Once it is signed off, an agreement is binding on all staff.

He finished his email by praising the efforts of teachers who attended a recent rally and wrote: “If I knew how to insert an emoji there would be hands clapping here - just picture it in your head.”

Asked by this newspaper whether he was suggesting to heads that they should mention early closure to councils on the grounds that such meetings would not be part of a WTA, Mr Flanagan said: “Yes if they are being told to hold a meeting. Staff can't be told to attend in their own time. Of course, a staff meeting may coincidentally have been planned.”

COSLA declined to comment.

A Scottish Government spokesman said: “The Deputy First Minister met with EIS this week where constructive and courteous discussions were had regarding the pay campaign. The Scottish Government intends to continue this positive dialogue throughout the process.

“The Scottish Government has worked with COSLA to put in place the best pay deal in the UK for 2018-19 and our joint letter accurately explains the component parts so that teachers have a full understanding of the proposals on the table.”