The police watchdog is facing fresh criticism after its report into the death of a black man who died in police custody found officers acted "reasonably" and "proportionately", while an inquest jury found unnecessary force had contributed to his demise.

Wednesday's Independent Police Complaints Commission report into the detention of Sean Rigg, who died after being restrained and arrested in 2008 in south London, followed the conclusion of an inquest into his death earlier this month at which the jury were highly critical of the police's conduct.

The jury at Southwark coroners' court found that police used unsuitable and unnecessary force against Rigg, with officers failing to uphold the detained man's basic rights as he collapsed after being pinned down for eight minutes.

The IPCC has announced an external review into its handling of the case, amid criticism from the family of Rigg, who say the police watchdog failed them. The IPCC accepted it had lessons to learn after its report showed it accepted accounts from officers about key aspects of the case that were later shown to be untrue or which the inquest jury disbelieved.

The central issue in the case was the police's restraint of Rigg. The IPCC report said: "There is no evidence to suggest that the officers who arrested Mr Rigg used excessive force. Conversely, however, there is evidence to show that the officers acted reasonably and proportionately during Mr Rigg's arrest and restraint."

In a statement Rigg's family said: "There has never been any doubt in our minds that the IPCC's inadequate report of February 2010 reflected an extremely poor and ineffective investigation into Sean's death.

"For the IPCC to conclude in their findings that 'the officers adhered to policy and good practice by monitoring Mr Rigg in the back of the van' is absolutely absurd, flies in the face of the evidence and clearly contradicts the jury's narrative verdict."

Rigg, 40, who had paranoid schizophrenia, was living in a south London hostel in August 2008 as his mental health deteriorated. One day he smashed up a gazebo and made karate moves that staff saw as threatening. They called the police, who did not initially respond to several pleas for help. Three hours after the first 999 call police responded, and three officers restrained Rigg.

The IPCC also said on Wednesday that two officers were under investigation over their evidence to the inquest and to investigators.

One of those is Sergeant Paul White, whose evidence to the inquest was contradicted by video evidence.

White claimed at the inquest to have checked on Rigg while he was detained in a police van, recalling the man's position and telling the jury other details. But CCTV evidence showed that White made no such visit and the officer later admitted what he said was not true. The other officer under investigation is Constable Mark Harratt.

In a foreword to the report, IPCC commissioner Amerdeep Somal said: "Since the conclusion of the inquest the IPCC has launched an independent investigation into the actions of the custody sergeant and a constable. This will consider the evidence Sergeant Paul White and Constable Mark Harratt provided to the IPCC during its original investigation and the evidence they gave, under oath, to the inquest."

The jury found that the Metropolitan police committed a catalogue of errors that "more than minimally" contributed to Rigg's death. Their narrative verdict was one of the most damning in recent times concerning a death in custody.

Somal added: "I have no doubt there are lessons for the IPCC from the investigation into Mr Rigg's tragic death. His family has demonstrated considerable determination and fortitude in seeking answers to the circumstances of his death and I acknowledge their sense of frustration with the IPCC investigation."

The IPCC added: "There is also concern about the treatment available for Mr Rigg once he had been arrested and taken to the police station. Our investigation records that it was 11 minutes before Mr Rigg was taken to the caged custody area from the van. After his collapse in that area, we were so concerned about the action (or inaction) of the forensic medical examiner (FME) that we reported him to the General Medical Council. He resigned as an FME shortly afterwards."

Somal said that half of all deaths in police custody in 2011/12 were of people with mental illness: "They represent a particularly vulnerable group, often, as in Mr Rigg's case, failed by the people and systems that ought to protect them," she said.

"As the IPCC has repeatedly stated, police stations are not, and cannot be, a 'place of safety' for people with mental health problems."

The IPCC has faced repeated criticism from families who have lost loved ones after contact with the police. The criticism has sapped the IPCC's credibility and it is facing an inquiry from MPs on the home affairs committee.

Helen Shaw of the group Inquest, which campaigns on deaths in state custody, said: "It should not have taken an inquest to discover some basic facts, such as the restraint of Sean Rigg in the prone position lasting several minutes, rather than seconds, according to officer accounts which were accepted by the IPCC."