The family of Lindsay Foreman, who is detained in Iran with her husband Craig, say they are "relieved" she was transferred to Tehran's Evin Prison after two months in a jail where several women died.
Demonstrations and hunger strikes broke out at Qarchak Prison where Ms Foreman had been held since August, after three women detainees died in September.
Ms Foreman was moved to Evin last week. That jail usually holds foreign nationals.
Her son Joe Bennett hopes the transfer will increase the chances of having a phone call with his mother, and “slightly better treatment”, despite its reputation for brutal conditions.
“We are relieved she’s out of Qarchak, but Evin is not a safe haven. We cannot let relief turn into complacency,” he said.
Former British-Iranian prisoner Nasrin Roshan, who was recently released from Evin, warned that access to medical care is difficult in the prison.
She suffered two blackouts before her release in May this year, and was saved by her cellmates who told the guards. The prison director accused her of attempted suicide.
“If my cellmates had not noticed in time I too would have become one of the regime's victims,” Ms Roshan told The National.
Mr Bennett and his family will meet British Foreign Secretary Yvette Cooper this week to demand that the government takes “immediate and decisive action” to bring the couple home.
“This meeting has to be about more than updates, it has to be about outcomes,” Mr Bennett said. “We need a clear plan from the UK government. They cannot allow this to drift any longer.”
He added there had been no verdict following the couple’s court hearing on 27 September, despite promises they would receive one within 10 days.
The Foremans, both in their early fifties, were arrested in Kerman in early January, as they travelled around the world on a motorbike. They have been charged with espionage, but their family have rejected the allegation and say they were tourists.
At least three women are believed to have died inside Qarchak prison in the past month due to the denial of essential medical services.
Among them was Somayeh Rashidi, who died of an epileptic seizure despite repeated requests for medical care from her family and cellmates.
“Knowing that people have died in the same place where Mum was held just days ago is unbearable,” Mr Bennett said.
Ms Roshan said prison authorities accused Ms Rashidi of “faking” her illness.
“She suffered from epilepsy and urgently needed medical treatment and medication, but the prison authorities not only did nothing, they accused her of faking it,” she said.
Ms Rashidi’s condition deteriorated after she was transferred from Evin to Qarchak “because of the extremely bad, unhygienic and substandard conditions, and because of the deliberate neglect and carelessness of the authorities,” Ms Roshan said.
