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
Kerrie Gosney brings you Sunday night's forecast
Rain moving through on Sunday evening, but Monday looks like one of the better days of the week ahead
The stakes are high for the Labour leader, writes Chris Ship - will another general election be on the cards in the coming months?