Separate investigations into three deaths in immigration removal centres (IRC) in the past month have been launched by the police, amid growing concern about the treatment of detainees.

The spate of deaths has caused alarm among critics of the government's detention policy, who warn that the system is at "breaking point" with poor healthcare putting people's lives at risk.

Two men died from suspected heart attacks at Colnbrook near Heathrow airport and the third killed himself at the Campsfield House detention centre in Oxfordshire on Tuesday.

John McDonnell, Labour MP for Hayes and Harlington, who has two detention centres including Colnbrook in his constituency, said he feared there would be more deaths as the system struggled to cope with the number of people being detained.

"The government is now detaining people on such a scale that the existing services are swamped," he said. "It is inevitable if we put the services under such relentless strain that there will be more deaths as a result … we are dealing with people who are extremely stressed and extremely vulnerable and the services are not able to cope and not able to guarantee their safety."

The first man who died was Muhammad Shukat, 47, a Pakistani immigration detainee who collapsed at around 6am on 2 July. His roommate Abdul Khan says that in the hours before he died Shukat was groaning in agony, had very bad chest pains and was sweating profusely.

Khan, 19, from Afghanistan, said he began raising the alarm around 6am and pressed the emergency button in the room 10 times in a frantic effort to get help.

Khan claimed that on three occasions members of the centre's nursing team entered the room and found Shukat on the floor where he had collapsed. Khan said they put him back into bed, took his temperature and some medicine was administered, but did not call emergency assistance immediately. According to Khan, the nurses initially said that Shukat could go to see the centre's doctor at 8am.

According to the London Ambulance Service, Colnbrook staff called an ambulance just before 7.20am. Attempts were made to resuscitate Shukat, but he was pronounced dead on arrival at Hillingdon Hospital.

A postmortem found the provisional cause of death to be coronary heart disease. Shukat's body has been returned to Pakistan and his family are understood to have no concerns about the medical treatment he received.

The second man to die at Colnbrook has not yet been named. According to the Metropolitan police he was 35 and was found dead in his cell at 10.30am last Sunday. London Ambulance Service officials pronounced him dead at the scene.

"A postmortem held on 1 August found the cause of death to be a ruptured aorta. The death is being treated as unexplained," said a police spokesman.

Colnbrook IRC is managed by Serco. In a statement to detainees about Shukat's death, deputy director at Colnbrook, Jenni Halliday, described her "deep regret" and extended her condolences.

In a statement to detainees about the second Colnbrook death, Serco's contract manager, Michael Guy, informed detainees that a resident in the short-term holding facility had died and that the death was thought to be from natural causes.

On Tuesday, a 35-year-old man hanged himself in the toilet block at Campsfield House detention centre in Oxfordshire.

A fellow detainee, who refused to give his name, said the man had been hours away from being deported and had become very anxious.

"He was normally a very quiet person … but the pressure is too much for people in here." It is understood the man had only been at the centre for a few days before he died. The Home Office refused to give any more details saying his extended family had yet to be informed.

Emma Ginn, from the campaign group Medical Justice, said the deaths had heightened concern about the poor healthcare on offer to those being kept in UK detention centres.

"Based on medical evidence from many hundreds of detainees, Medical Justice has documented the disturbingly inadequate healthcare provision that often vulnerable immigration detainees are subjected to in Colnbrook and other immigration removal centres... [this] combined with the perilous and frightening conditions of detention, is a lethal cocktail, a disaster waiting to happen."

The UK Border Agency declined to comment on the specific circumstances of each case. It said the police and the Prisons and Probation Ombudsman always investigated deaths in immigration detention centres and it would be inappropriate to comment until these were complete.

David Wood, director of criminality and detention at the UK Border Agency, said all detainees at immigration removal centres have access to health services seven days a week.

"All detainees are seen by a nurse within two hours of arrival and are given an opportunity to see a GP within 24 hours," he added. "The health of all detainees is monitored closely, and the healthcare professionals are required to report cases where it is considered that a person's health is being affected by continued detention.

"The UK takes its responsibilities seriously, which is why we consider every case on its individual merits and will continue to offer protection to those who need it. However, detention is an essential part of our controls on immigration in the UK."

A groundbreaking ruling

A man with severe mental illness was unlawfully locked up in a UK detention centre for five months and subjected to inhuman or degrading treatment, according to a high court ruling.

The man, a 34-year-old Indian national, was detained in Harmondsworth immigration removal centre between April and September last year.

On Friday a judge ruled that his treatment amounted to a breach of article 3 of the European convention human rights. The man's lawyer said the ruling – thought to be the first of its kind – raised wider questions about how the government treats people with mental illnesses in the immigration and detention system.

"The court's decision that my client suffered inhuman or degrading treatment at a UK detention facility sends a very loud and clear message to the authorities," said Jed Pennington from the solicitors Bhatt Murphy. "We would urge the minister to conduct a fundamental review into how people suffering from mental illness are treated in the immigration detention estate."

The man, referred to as "S" in the ruling, had a history of serious ill treatment and abuse before arriving in the UK. He served time in prison for wounding and assault before being transferred to a secure psychiatric hospital until his discharge in April 2010.

Following his release the UK Border Agency said there was "no evidence" he was mentally ill and he was detained in Harmondsworth where his health deteriorated and he began to have psychotic episodes and self harm. The high court intervened and he was released on bail. His lawyers said he had been living with his family since then and had fully complied with the conditions of bail set by the court.

In the ruling judge David Elvin said: "S's pre-existing mental condition was both triggered and exacerbated by detention and that involved both a debasement and humiliation of S since it showed a serious lack of respect for his human dignity. It created a state in S's mind of real anguish and fear, through his hallucinations, which led him to self-harm frequently and to behave in a manner which was humiliating…"

A UK Border Agency spokesperson said: "We regularly review our detention policies and will look at the findings in this case to ensure lessons are learned. Detention is an essential part of our immigration control but we recognise the importance of ensuring it remains appropriate on a case by case basis."

• This article was corrected on 30 August 2011, attributing the quotes in the fifth paragraph from the end to Jed Pennington from Bhatt Murphy solicitors