Three prisoners have now died after contracting the virus and another 69 inmates and 14 prison staff have tested positive for COVID-19 across 25 prisons in the country.

Assange was denied bail last week after his lawyers failed to convince District Judge Vanessa Baraister he was a vulnerable person at higher risk of the disease inside Belmarsh prison.

The country's prisons are currently locked down and 69 pregnant women and women with babies have been released early to mitigate the virus.

UK's former chief inspector of prisons David Ramsbotham says there must a full scale release of short-term prisoners.

"The remand prisoners in particular should be let out," Baron Rambotham wrote in the Telegraph newspaper.

"They should also examine indeterminate sentence prisoners."

Professor Richard Coker, from the London School of Hygiene and Tropical Medicine, has written two reports on coronavirus in Britain's prisons in the past week.

He says if alternatives to prison, like house arrest, are feasible they should be used.

"Preventing an outbreak is much easier than controlling an outbreak," Prof Coker wrote.

"The risk to any individual is likely to be much lower in the wider community, where social distancing is feasible, than in a place that is, by definition, a congregate setting."

WikiLeaks ambassador Joseph Farrell says Assange, who's fighting extradition to the US, shouldn't be in prison as he hasn't committed a crime in the UK.

"He shouldn't be in Belmarsh which is a ticking time-bomb considering this pandemic," he told AAP.

"He should be with his family in this hour of need."

Local MP Abena Oppong-Asare is concerned prison staff and inmates, particularly those at Belmarsh are unable to socially-distance or self-isolate.

The Labour politician hasn't received any response to a letter outlining her concerns sent to Minister of State for Prisons and Probation Lucy Frazer five days ago.

"Inmates should be afforded the same rights and protections as the wider public," Ms Oppong-Asare told AAP on Friday.

She called for personal protective equipment to be provided to prison staff and for testing to ramped up at Belmarsh and other prisons.

Britain's two leading prison advocacy groups - the Howard League for Penal Reform and the Prison Reform Trust - also want Secretary of State for Justice Robert Buckland to safely release as many prisoners as possible to stop the "loss of life on an unprecedented scale".

"The public has understood and accepted extraordinary changes in the normal workings of society because of the government's strict policy of following the best scientific and medical advice," the charities wrote.

"It is crucial that the same principle should apply to decisions relating to prisons and prisoners."

The US government is trying to extradite Assange to face 17 charges of violating the Espionage Act and one of conspiring to commit computer intrusion over the leaking and publishing of thousands of classified US diplomatic and military files.

Some of those files revealed alleged US war crimes in Iraq and Afghanistan.

The charges carry a total of 175 years' imprisonment.

Assange's next extradition case is set for April 7.

Australian Associated Press