"Unless the committee is prepared to take the steps to enable Mr Brownett to fulfil his promises to me, I will have no alternative but to stand down as captain," Cork insisted.
"I have tried to be reasonable and patient, and I have deliberately avoided confrontation, but my position has now become so compromised that I can accept it no longer.
"There is no way that I will continue as captain if Rhodes and Hayhurst continue to exercise an influence over playing matters."
Cork became Derbyshire captain at the end of the 1997 season, when the county was in turmoil following the resignation of their then-captain, Dean Jones. Last season, harmony was restored and performances improved as Derbyshire reached the final of the NatWest Trophy.
Cork added: "The authority on playing matters, which I was publicly promised by Mr Brownett, has been challenged and overturned by others within the committee."
Brownett yesterday promised to back Cork, saying: "He will be captaining Derbyshire next season if I have anything to do with it."
Rhodes, who was voted back on to the committee last winter after resigning two years ago, said: "The decisions were reached democratically, initially by the cricket committee and then ratified by the general committee."Reuse content