The police chief who led the sexual abuse investigation into the late former prime minister Sir Edward Heath has resigned following “serious allegations” about his behaviour.

Mike Veale, the chief constable of Cleveland police, had been under pressure since a police watchdog investigation found in September that he had lied about a smashed mobile phone.

But on Monday, Barry Coppinger, the Cleveland police and crime commissioner, said he had been made aware of allegations of a “serious nature” that had been referred to the Independent Office for Police Conduct (IOPC).

Coppinger gave no more detail on the allegations, but said Veale had resigned with immediate effect on Friday.

His resignation came months after Veale apologised after the IOPC found he had lied about how he had broken his work phone.

Veale told colleagues he had smashed the device when he dropped it in a car park and it was run over. But an investigation discovered he had destroyed the phone when he played a poor shot during a round of golf and hit his bag with a club in frustration.

The IOPC investigation was launched after anonymous claims – later found not proven – that he had smashed his police-issue phone to hide contacts with “various parties” during the Heath inquiry.

The IOPC concluded Veale had a case to answer for misconduct for providing an inaccurate account of the incident, but Coppinger chose to resolve the case with “management action”.

However, the incident cast a shadow over Veale’s time at Cleveland police, which appointed him as chief constable in March 2018 while the IOPC investigation was continuing.

Ben Houchen, the Conservative mayor of Tees Valley, called for Coppinger to resign. “To appoint someone under investigation and under such a dark cloud nationally was more than a mistake – it was reckless and incompetent. I said this at the time but was shouted down by the police commissioner,” he said.

“The chief constable merry-go-round must come to an end and our police commissioner must resign. Until Mr Coppinger steps aside, Cleveland police cannot recover.

“We must have leadership in this uncertain time to make sure that officers feel supported, and Mr Coppinger has shown year in, year out that he is incapable of carrying out the role that he holds.”

Houchen, who has previously called for Cleveland police to be disbanded, said he had written to the home secretary, Sajid Javid, to request an urgent meeting about the force’s future.

Simon Clarke, the Conservative MP for Middlesbrough South and East Cleveland, called for a “root-and-branch review” of Cleveland police that would leave “all options on the table”.

Cleveland police have faced investigations over racism, accusations of discrimination and bullying, complaints from senior officers, and a ruling that they breached the human rights of journalists they spied on using anti-terror legislation.

Coppinger said he would appoint an interim chief constable shortly. “As an organisation, Cleveland police have undergone a comprehensive programme of transformation and improvement, which has been recognised by Her Majesty’s Inspectorate of Constabulary and Fire and Rescue Services. I am determined to ensure this progress will continue as I look to recruit a permanent replacement,” he said.

“I want to reassure our communities that the same dedicated and compassionate officers and staff, who bravely serve the people of Cleveland every day, will continue to work hard to keep you safe.”