A leaked audit of the 457 scheme by the Fair Work Ombudsman, obtained by Fairfax Media, suggests that up to 3600 people are working as teachers, mainly in early childhood care.

Rules governing 457 visas state they should only be granted when an employer "cannot find an Australian citizen or permanent resident to do the skilled work" required.

Half of all teaching graduates – about 8000 people – had not found permanent employment four months after completing their education training last year, Fairfax revealed on Monday.

But the unredacted version of the Fair Work Ombudsman's audit – which looks in detail at roughly 1 per cent of the 200,000 such visas on issue – shows that childcare centres and some specialist schools are importing teachers.

And they are not confined to regional areas that struggle to attract workers.

A childcare centre on Collins Street in the Melbourne central business district has two teachers on 457 visas, according to the Fair Work log.

In Sydney, centres in Crows Nest, Artarmon and Balmain have imported staff.

Montessori schools in the ACT and South Australia have employed teachers on 457s. The Australian Islamic College in Booragoon, Western Australia, has three staff on 457s, while the Sholem Aleichem College in Elsternwick, Melbourne, imported a Hebrew teacher.

Charles Sturt University in NSW and the University of Western Sydney have up to six lecturers and tutors on the visa.

Stephen Dinham, professor of education at the University of Melbourne, said non-traditional colleges were turning out graduates, particularly in early childhood and primary, worsening the glut of university-trained teachers.

He said the dozen or so different routes into early childhood teaching, from a minimum-level TAFE diploma up to a master's in education from a university, made understanding the sector more complex than primary and secondary schools.

Unions have blamed the need for foreign staff on the "inadequate" pay in the female-dominated early childhood sector.

"The fact that early childhood employers are resorting to importing teachers on 457 visas when there is a huge oversupply of graduate teachers will not come as a surprise to anybody involved in the early childhood sector," said Lyndal Ryan, national vice-president of United Voice.

"At the root of this problem are the inadequate wages in the sector. There is a well-established pattern of qualified teachers working in ECEC [early childhood education and care] until they can get a position in the school system because schools pay better, the hours are shorter and there are longer holidays."

United Voice estimates that 180 people abandon jobs in the early childhood sector every week. The industry is the most female-oriented of all, with more than 95 per cent female representation.

Jo Briskey, acting executive director of early childhood advocacy group The Parenthood, also linked wages to the supply imbalance.

"Parents want their kids to get the best-quality education experience from the highest-quality educators," she said. "That doesn't mean that someone who has trained overseas is not qualified to work here in Australia but if wages were more closely aligned between primary and early childhood you would be able to attract more trained Australians and go some way to balancing the oversupply of teachers."

The Productivity Commission, in a draft report into childcare, released in July, signalled dropping the required qualifications required to work with children aged three and under. Groups such as The Parenthood and the Australian Research Alliance for Children and Youth are resisting that.

The report, a final version of which will be delivered to government this month, also advocated government subsidies for nannies to ease the pressure on childcare centres.