Police are to be investigated over allegations that they placed under "improper" surveillance the sister of ex-paratrooper Christopher Alder, who died on the floor of a police station.

Janet Alder has spent years campaigning to find the truth behind one of the most controversial deaths in police custody. Her barrister is also alleged to have been put under surveillance, raising questions over the ethics of police monitoring of lawyers. The espionage is alleged to have happened at the time of the inquest that found Christopher had been unlawfully killed in April 1998.

CCTV footage showed the 37-year-old father-of-two gasping for breath as officers chatted and joked around him. The film showed that while he was fighting for his life, he received no help from five officers, who believed that he was play-acting. It took 11 minutes for him to stop breathing. As he lay dead, monkey-like noises could be heard on an audio tape.

Evidence of the espionage has been uncovered by police and shared with the Independent Police Complaints Commission (IPCC), which announced an investigation on Friday.

The inquiry comes after police forces across England and Wales were ordered to search their archives for evidence showing that the family and supporters of murdered teenager Stephen Lawrence were put under surveillance by police.

The trawl was ordered by the home secretary, Theresa May, after the Guardian revealed that undercover police gathered intelligence on his family and campaign groups while they were pressing for a proper investigation into his racist killing in 1993.

The IPCC did not make clear why evidence of the alleged surveillance of Janet Alder and her barrister, Leslie Thomas, was found during the search for documents about the Lawrences and their supporters.

On Friday, the IPCC also announced it was investigating former police chief Sir Norman Bettison over claims that he attempted to undermine a witness who gave evidence at the public inquiry, led by former judge Sir William Macpherson, into police failures in the investigation of the Lawrence murder.

The witness, Mohammed Amran, has said that he was going to denounce police racism in the West Yorkshire force, where Bettison was a senior officer when dossiers were allegedly compiled on him.

The IPCC said "the intelligence-gathering requested appears to have been both inappropriate and intrusive", adding that police databases may have been misused. The watchdog said it would investigate whether commissioning a report on the witness to the inquiry was racially motivated.

The IPCC investigation into the alleged surveillance of Alder and her barrister by Humberside police is the latest development in a saga of official failures.

A Falklands veteran, Alder died while handcuffed on the floor of a Hull police station. An inquest in 2000 returned a verdict of unlawful killing. In 2002, five police officers were put on trial for manslaughter and misconduct in public office, but were cleared of all charges on the orders of the judge at Teesside crown court.

A previous investigation by the IPCC ruled that four of the officers present in the police station at the time were guilty of the "most serious neglect of duty". It was a conclusion that was disputed by the Police Federation, the police trade union.

Humberside police gave an apology to the family for "our failure to treat Christopher with sufficient compassion and to the desired standard that night".

In 2011, it was revealed that Christopher's family had buried the wrong person when his body was discovered in a hospital mortuary. Hull city council could not explain why an elderly woman had been mistakenly buried in his grave. Two years ago, the government apologised to his family for a series of human rights violations.

On Friday, the IPCC announced it was not going to investigate the Metropolitan police over allegations made by Peter Francis, a former undercover officer, that he was asked to find information that could be used against members of the Lawrence family after their son was murdered.

Instead, the watchdog has decided to leave the investigation to an internal police team led by Mick Creedon, the Derbyshire chief constable, and a barrister, who have been asked to examine the claims.The IPCC said it had not assessed the claims and had asked to speak to Francis, who had not yet responded. It had written once, on July 16, to Francis, who has been considering his response. Like Doreen and Neville Lawrence, the parents of the murdered teenager, Francis has said that he has no confidence in the internal police investigation. They have all called for a judge-led public inquiry where, Francis said, he will give evidence on oath.

The watchdog has announced it will not investigate two other forces, Greater Manchester and South Yorkshire, over allegations that they carried out surveillance on groups and individuals attending the Macpherson inquiry.