The mayor of Middlesbrough, Ray Mallon, has written to the Justice Secretary appealing for the government to make Teesside's coroner resign.
ITV News has had exclusive access to the letter which asks Mr Grayling to secure Mr Sheffield's removal from office.
"Mr Sheffield is accountable to no-one. And what I want Mr Grayling to do is intervene and remove him from his post immediately.
"It's the case that people have got to move on. He's been there over 40 years, and what I'd like to see is somebody new come in with new ideas."
There have been repeated calls for Michael Sheffield to step down, after it was found that the Teesside coroner's service had up to 300 families waiting for inquests at any one time.
Mr Sheffield had written to police requesting more resources, as the force staffs part of the coroner's service.
Since a review by the local council Cleveland Police have put in more staff, temporarily, and that backlog has now been reduced.
Another review by the probation service is underway and the force has promised to stick to the recommendations it makes.
"We are just over one month into the review and it is progressing well.
"We have seen a reduction in the backlog, and the staff within the office continue to work hard to deliver the service that supports bereaved families on Teesside."
More top news
Clear weather develops overnight into Monday. Cold days and frosty nights. Mainly dry inland - but a wintry risk continuing in the east
Icy first thing and windy, with wintry showers lingering further south, especially at the coast. Brighter elsehwere
Emma brings you Saturday's forecast