Hundreds of thousands of pupils faced disruption to classes today as one of the UK's biggest teaching unions staged a one-day walkout as part of an increasingly bitter dispute over pay and conditions.

Schools across England and Wales were affected by the National Union of Teachers (NUT) strike, forcing many to close their doors to some or all students.

But as members began the walkout, there were indications that relations between the NUT and fellow teaching union the NASUWT - which together have been running a joint campaign of industrial action - have become strained.

Both unions took part in a series of regional strikes in the autumn term, but the NASUWT decided not to take part in today's national action.

A leaked memo signed by NASUWT general secretary Chris Keates claims that some members have faced threats, insults and intimidation from members of the NUT.

The document, sent to senior local NASUWT officials, which has been posted on social networking websites, says NASUWT members should not cover for NUT staff who are taking part in the strike.

But it adds: "T he onus is on the NUT to challenge headteachers who seek to undermine their strike action. It is not the responsibility of the NASUWT and its members to make the NUT action successful."

The memo goes on to say: " We should not tolerate any threats, insults or attempts to intimidate our members or activists by the NUT. Unfortunately, in some areas, this has been a hallmark of the activity to date. The NASUWT, as an independent trade union, has made its decision with regard to industrial action strategy and that should be respected by a sister trade union."

It also accuses the NUT of running "abusive social media campaigns" and making "aggressive accusations" about the NASUWT.

The memo does also say that the NASUWT remains " committed to the joint declaration and seeking to work with the NUT".

An NUT spokeswoman insisted that the union had not been running a national campaign against the NASUWT.

"There has been no national campaign against NASUWT members regarding strike action," she said.

"There has been no negative campaigning from the national NUT headquarters and the NASUWT has not brought this to our attention. We continues to engage in talks with Government alongside the NASUWT and other teacher unions to resolve the very pressing issues that face the teaching profession."

An NASUWT spokesman declined to comment on the memo or the NUT's strike action.

As NUT members joined marches, rallies and picket lines across England and Wales, union leaders said the early indications were that the strike is well-supported.

NUT general secretary Christine Blower said: "Certainly the message we are getting is that the action is well-supported. On the back of the 60-hour week workload diary survey teachers are just feeling overwhelmed."

She said rallies and marches are taking place all over the country and that "people will be out and about".

Ms Blower said the NUT has been staging events around the country on a weekly basis for some time to tell the public about their campaign and the issues they are highlighting.

"We are saying that very bad things are happening to education and (Education Secretary) Michael Gove needs to listen."

The NUT's bitter dispute with the Government focuses on three issues - changes to pay, pensions and workload.

The action has been condemned by the Department for Education (DfE), which says that it will disrupt parents' lives and damage children's education.

The DfE has said parents will "struggle to understand" why the NUT was pressing ahead with its strike.

A spokesman said: "They called for talks to avoid industrial action, we agreed to their request, and talks have been taking place weekly.

"Despite this constructive engagement with their concerns, the NUT is taking action that will disrupt parents' lives, hold back children's education and damage the reputation of the profession."

Yesterday, David Cameron's official spokesman said the Prime Minister would call on teachers not to strike because the action "disrupts children's education and children's families".