Top civil servant rejects probe into Andrew Mitchell rant DEMANDS for a full Whitehall investigation into chief whip Andrew Mitchell's angry confrontation with Downing Street police have been rejected. Cabinet Secretary Sir Jeremy Heywood said he had agreed with Prime Minister David Cameron there would not be "any purpose" in having an inquiry after Mr Mitchell apologised for the incident. In a letter to shadow home secretary Yvette Cooper, the top civil servant wrote: "There clearly remains a genuine difference of view about what words were actually used. But Andrew Mitchell has acknowledged that his words and behaviour were inappropriate and he failed to show proper respect for the police. The news came with Mr Mitchell still struggling to draw a line under last Wednesday's episode, when he is said to have launched a foul-mouthed tirade at officers who stopped him riding his bicycle out of the main Downing Street gates. The chief whip reiterated his regret when he ventured in front of cameras for the first time yesterday morning. However, he pointedly refused to answer questions about whether he had branded the police "plebs" - as their leaked written records of the exchange suggest. In the letter, Sir Jeremy revealed that the head of security at No 10 and the Prime Minister's principal private secretary, Chris Martin, had spoken to the police sergeant involved. "The Prime Minister spoke to Andrew Mitchell and made very clear that his behaviour fell short of what he expects of his ministers," Sir Jeremy wrote. [Mr Mitchell] then phoned the police officer in question to apologise personally and he has since reiterated his apology in public. The officer has accepted his apology. The Scotsman understands Mr Cameron has a potential replacement lined up for Mr Mitchell. Government sources have revealed that Ludlow MP Philip Dunne is being considered for the role of chief whip. However, a decision is not expected until after Mr Cameron returns from his trip to the United States. The Prime Minister is scheduled to fly out to New York on Tuesday.