A refugee and torture survivor who has been incarcerated in “hellish” conditions by the Australian authorities since 2013 has appealed to be allowed to join his sister in the UK.

In the first case of its kind, Thiraviyarajah Subramaniyam, 37, a Tamil from Sri Lanka, appealed in the UK immigration tribunal on Tuesday against a Home Office refusal to allow him family resettlement in the UK.

He is suffering from serious mental health problems as a result of torture he experienced in his home country followed by years of detention when he sought sanctuary in Australia, first on Christmas Island in 2013 followed by an extended period of detention on Manus Island in Papua New Guinea. He is currently in the East Lorengau Transit Centre on Manus.

Amnesty International has reported on “hellish” conditions at the Manus camp. One Somali refugee was briefly hospitalised and then discharged after setting himself on fire at the centre on Monday.

Dozens of suicide attempts and self-harm incidents have been recorded among refugees on Manus Island since the re-election of the Australian coalition government last month. The refugees had been hoping a Labor government would be elected that would speed up their resettlement in third countries.

In a statement to the court Subramaniyam’s 36-year-old sister Susila Subramaniyam, a supermarket worker who lives with her husband and son in High Wycombe, Buckinghamshire, said her brother has suffered for years as a result of his detention by the Australian authorities.

“My brother is a refugee and is currently caught in a state of limbo in Papua New Guinea where he is being held until he is granted entry to another country.”

She said that she and her family are willing and able to look after and support her brother who is suffering from “poor and deteriorating” mental health.

“I’m very scared for my brother’s future if he’s not able to come and stay with us. He’s not able to look after himself properly,” she said.

His lawyers said his case was “exceptional” when he applied to come to the UK in December 2017. But the Home Office rejected the case in June 2018 saying he failed to provide a valid passport. As a refugee, he does not have a valid passport from his home country but he does have a UNHCR issued travel document recognising him as a refugee.

Rebecca Lim, a community activist based in Australia who has visited Subramaniyam and is supporting him, expressed concern for his deteriorating health.

Speaking from Australia, she told the Guardian: “Healthcare conditions on Manus are just horrendous. They can treat malaria and typhoid but not torture and trauma. There have been 40 cases of self-harm and attempted suicide since the elections. There’s no plan B if Thiraviyarajah isn’t able to get to the UK.

“If he is allowed to come, he will be the first one to get there from one of these detention centres. He’s a single man. He hopes to marry and have a family. He says he would like to get a job as a truck driver. He wants a future.”

His solicitor, Naga Kandiah of MTC Solicitors, said: “Despite having applied within Home Office guidelines his case was refused. His deteriorating mental health problems are a result of the lethal combination of being a torture survivor and the appalling conditions he has been held in on Manus Island.”

Judgment has been reserved following Tuesday’s hearing. The Home Office refused a request to comment on the case.