A teacher was given an official target by her school to sound "less Cumbrian", according to her union representative.
Paul Watkins from the NASUWT said it was the most "bizarre and extreme" target he had ever seen in his career.
Education watchdog Ofsted said negative comments about regional accents would be "clearly inappropriate".
The woman, who taught in west Berkshire, is said to have taken the request, made following an Ofsted inspection, in "good humour".
Mr Watkins said he learned last week the teacher had been given the official target to "sound less Cumbrian".
"We should be celebrating diversity," the national executive member from the NASUWT said.
'Up in arms'
"I work with somebody from Wales. What about people with Bangladeshi or Polish accents? I think all of them are acceptable."
The teacher herself did not make an official complaint to the NASUWT.
Mr Watkins would not identify the school or the teacher involved, but said the target was set by the school in response to a comment by an Ofsted inspector during a recent inspection.
Reading University professor of phonetics Jane Setter said: "We are all up in arms over this. We couldn't believe it. It's devaluing local accents."
An Ofsted spokesman said: "We would be happy to look into this matter if we are told the name of the school.
"Inspectors comment on the standard of teaching at schools. Negative comments about the suitability of regional accents are clearly inappropriate, and should form no part of our assessment of a school's or teacher's performance."
A spokeswoman for West Berkshire Council said schools in the area employed "high quality staff from all over the UK and beyond".
"These colleagues are an asset to our children's learning, and the variety of accents and dialects they bring adds value to the diversity in ways of speaking that schools celebrate," she said.
"We are unaware of the case highlighted, so the facts remain unclear, but seems to have emanated from a comment made by an Ofsted inspector.
"If it is true, we assume this is a personal observation by that individual, which seems to have been taken literally."