A detainee in Villawood detention centre has been tested for coronavirus, as asylum seekers and refugees in immigration detention centres across Australia say it is impossible for them to self-isolate and protect themselves from the virus.

“We are sitting ducks for Covid-19 and extremely exposed to becoming severely ill, with the possibility of death,” detainees from across immigration detention centres have written in a letter to prime minister Scott Morrison, pleading to be released into the community on health grounds.

Asylum seekers and refugees said they were “anxious and scared” of a Covid-19 outbreak inside detention, saying they were being held “in a potential death trap in which we have no option or means to protect ourselves”.

The Australian government’s own advisory says “people in detention facilities” are considered most at risk of serious infection of Covid-19. Visits to immigration detention centres – including by family members – have been cancelled.

In the UK, the Home Office has released more than 300 people from detention because of the Covid-19 pandemic.

Domestically, the Australasian Society for Infectious Diseases (Asid), the Australian College of Infection Prevention and Control (ACIPC) and Doctors for Refugees have all said detainees need to be released from held detention urgently to prevent rapid Covid-19 transmission.

“Keeping people unnecessarily locked up in close confinement at this time when the rest of the country is being urged to stay in their own four square metres is not only cruel, callous and highly discriminatory, it is potentially exacerbating a public health crisis,” said Dr Barri Phatarfod, co-founder of Doctors for Refugees.

A public petition from Human Rights for All calling for the immediate release of asylum seekers and refugees in detention has attracted nearly 20,000 signatures.

“Families across Australia are struggling with the ramifications of Covid-19,” director-principal Alison Battisson said.

“The families of people in detention are no different. We ask that these families are allowed to bring their loved ones home to see out the pandemic. These people have safe and caring home environments willing to support them, either with a family member or advocate in Australia.”

A spokesman for the Department of Home Affairs told Guardian Australia there were no confirmed cases of Covid-19 at Villawood immigration detention centre or within the broader detention network.

“Infection control plans are in place and plans to manage suspected cases of Covid-19 have been developed and tested.”

A male detainee has been isolated in the Blaxland wing of Villawood detention centre after being taken to hospital to be tested for Covid-19. The results of his tests are unknown.

His test follows that of another asylum seeker tested in Melbourne’s detention centre, and the positive Covid-19 result of a Serco guard working at the Brisbane hotel where asylum seekers and refugees are being detained.

Doctors said there were almost no infection controls inside detention centres, where toilet paper, soap and hand sanitiser are running short, and those in detention have to queue in close proximity for meals and other services.

People are still being detained in shared and bunk rooms, with up to four people in a room in some detention centres.

Thirty-one-year-old Huyen Tran, a Vietnamese asylum seeker, is the mother of an Australian-born daughter, Isabella, who has lived almost all of her life inside the Melbourne Immigration Transit Accommodation (Mita) centre.

Isabella was taken to hospital in July last year with influenza after IHMS staff at Mita failed to immunise the then 15-month-old.

Dr Barri Phatarfod said: “[Isabella’s previous illness] is quite a serious condition when children are that young and their lungs are still developing. We don’t know if she has residual damage to her lungs as a result and if so, this would make her particularly susceptible to coronavirus infection.”

Speaking to Guardian Australia, Tran said Isabella was meant to have a doctor’s appointment last Friday because the toddler had been coughing and had a runny nose but staff failed to take her to the appointment. Medical notes seen by Guardian Australia indicate the toddler has lost weight and is waiting for a referral to a paediatric dietician.

In a joint statement, Asid president Joshua Davis and ACIPC president Philip Russo said 1,400 asylum seekers and other non-citizens were being held in detention in crowded conditions that would preclude adequate social distancing or self-isolation. Staff would also be at risk from an outbreak.

“We urge the commonwealth government to consider the release of detainees into suitable housing in the community if they do not pose a significant security or health risk.”

Social distancing impossible in a crowded immigration detention facility. This puts us all at risk. Aus Society for Infectious Diseases recommends community detention for low-risk immigration detainees. We must listen. ASID are our experts on #COVID19Aus. https://t.co/GuDfx5s5wy — Edward Santow (@esantow) March 21, 2020

In a collective letter from inside detention, detainees said they feared the virus would be brought in from outside the centre, and would be uncontrollable once inside.

“The staff are on a continuing rotation roster which we believe to be unacceptable as this causes an exceedingly high potential for Covid-19 to be transported within detention centres. The centre’s are drastically medically under-resourced. There are not enough doctors, nurses or resources to tend to us should an outbreak occur.”

The Refugee Council of Australia has urged the government, as part of its economic stimulus measures, to extend supplementary payments to all people living in the Australian community, including those on bridging visas, who face losing their jobs in the economic downturn.

A spokesman for the Department of Home Affairs said there were established plans for dealing with a potential coronavirus outbreak within the detention network.

“Within the detention facility detainees displaying any Covid-19 symptoms may be quarantined and tested in line with advice from health officials and in accordance with the broader commonwealth response.

“A range of measures have been introduced, and are being continually reviewed, to keep detainees and staff informed of preventive measures and personal hygiene standards.”