The National Union of Teachers and senior staff in the General Teaching Council for England want the profession to be on the same footing as doctors, lawyers and police, whom it has long been illegal to impersonate.
Those caught pretending to be teachers - perhaps by talking in staffroom jargon or ironing leather patches on to their jackets - would face fines or imprisonment.
Baroness Walmsley, a Liberal Democrat peer, attempted to amend the Education Bill in the House of Lords last week to include the legislation.
She acknowledged that, in Britain, people seemed more likely to impersonate doctors than teachers.
"There must be something rather glamorous about the medical profession that attracts unqualified people to masquerade in a white coat with a stethoscope around their neck," she said.
"Doctors have their patients' lives in their hand. But teachers also have children's lives in their hands."
The NUT has been considering pressing for the legal sanction for some time but said the need for it had been highlighted by a series of cases of teacher-impersonators in America, including three in Oregon whose credentials were revealed to be fake in 2002.
The House of Lords amendment was withdrawn after Baroness Andrews, a Labour peer, argued that safeguards already existed to stop unqualified people working in schools. "Teachers cannot just set themselves up as such," she said. "They must apply for a post, which means having references taken up and checked."
Undeterred, the NUT said it would continue to push for teachers to be treated in the same way as lawyers, doctors and the police.
John Bangs, the union's head of education, said: "It's a status issue."