Two police officers whose evidence on oath about the death of a man in police custody was contradicted by CCTV evidence will not face criminal charges, prosecutors have said.

The officers were investigated following the death of Sean Rigg, a musician who died in 2008 after being arrested and restrained by police in south London.

Sgt Paul White and PC Mark Harratt were arrested on suspicion of lying at an inquest into the death of Rigg, and during interviews with investigators from the Independent Police Complaints Commission (IPCC).

An inquest jury in 2012 found police actions had contributed to Rigg’s death, after he was held down in a V shape in a prone position for eight minutes. The inquest verdict followed a flawed first IPCC investigation, which exonerated officers.

White claimed at the inquest to have checked on Rigg while he was detained in a police van on arrival at Brixton police station. But CCTV evidence showed he made no such visit and the officer later admitted what he said was not true. Harratt had supported the sergeant’s account.

Marcia Rigg, sister of Sean Rigg, said: “My family is surprised and bitterly disappointed by today’s announcement … We categorically do not accept this decision, which only serves as further upset and anguish. We regard the evidence as compelling and strongly believe that a jury should have been given the opportunity to make a decision on the evidence. The public’s confidence in the British criminal justice system is tarnished by decisions like this.”

In its published reasoning, the CPS said the prosecution would have to prove the officers were lying and not simply mistaken. Their review of the material concluded there would be insufficient evidence to prove a case against the officers for perjury or conspiracy to pervert the course of justice.

The CPS said White was never challenged by the IPCC over his account of what happened, even after CCTV showed his account was wrong.

The CPS said: “At no point during the investigation was the custody sergeant challenged on his memory or made aware of the relevant section of CCTV which undermined his statement. In such circumstances, we take the view that a jury would be likely to accept that this confirmed in the custody sergeant’s mind that his memory was correct.

“Furthermore, there is evidence to suggest that he has a medical condition which impacts on his memory, which is relevant given what the evidence suggests about the number of occasions on which he may have attended prisoners in the yard and the passage of time between the incident and the first interview.”

The CPS said White’s evidence to the inquest jury was based on his interviews with the IPCC four years earlier, and they could not disprove his account that he had come to believe his recollection was correct, in part because in had never previously been challenged.

The CPS had similar reasons for not bringing charges against PC Harratt.

The IPCC’s own review into its botched initial investigation found “interviewers at times appearing hesitant to put to the officers fundamental questions about how they exercised their duty of care”. It also found the IPCC was too soft in challenging police accounts.

The inquest jury’s findings led to the IPCC commissioning a review of its first investigation, which was found to be flawed. Its conclusions exonerating the police were dropped and a new inquiry started. The review found IPCC investigators had accepted accounts from officers that were “improbable” and “implausible”.

Daniel Machover, solicitor for the Riggs, said the family was very disappointed.

Malcolm McHaffie, CPS deputy head of special crime, said: “We appreciate that this decision may be disappointing to the family of Mr Rigg, but we have written to them to explain our position in detail and have offered to meet with them if they so wish.”

An IPCC criminal investigation into any other charges over the death continues. That is believed to be investigating any offence relating to misconduct in public office and be examining the actions of another five officers.

The inquest jury found that police used unsuitable and unnecessary force on Rigg, with officers failing to uphold the detained man’s basic rights as he collapsed after being pinned down. They concluded the Metropolitan police made a catalogue of errors that “more than minimally” contributed to Rigg’s death.

Rigg, 40, was a musician who suffered from paranoid schizophrenia. He was living in a south London hostel in August 2008 as his mental health deteriorated. One afternoon he smashed up a gazebo and made karate moves that staff viewed as threatening so they called police.