The initiative by Bristol City Council, which offers two candidates a two-year placement with the local authority, is only open to people from black or ethnic minority backgrounds. The scheme, which is advertised on its web site, states simply ‘Open to Black and minority ethnic graduates’.

Officials said that the Race Relations Act 1976 allowed for public authorities to offer training to specific groups of people if they were under-represented.

James Easey, a spokesman for Bristol, told the Daily Telegraph: “This is the third year of running the traineeship and it was started because of the marked under-representation of ethnic minority people in the council’s workforce.”

The normal recruitment process was not rectifying “this unacceptably low trend”, which meant there was a “strong case for this small positive recruitment traineeship”, he added.

“Graduates from any ethic background are open to apply for the national graduate local government programme, which we recruit from every year – we have just recruited two graduates in this way,” Easey said.

The local authority employs 9,000 workers, of which 8,370 are white and 630 or 7% are from ethnic minorities. Some 12% of Bristol residents come from minority backgrounds, however.

But one white jobseeker, who asked not to be named, said the move was “totally racist” and would have been “an excellent opportunity for me to make use of the skills and qualifications that I’ve acquired”.

“But by being white, I’m excluded from applying for the post. Surely equal opportunities means giving everyone an equal chance to succeed rather than discriminating against people because of the colour of their skin,” he added.