WikiLeaks warned about the situation at the facility, where its founder Julian Assange is now imprisoned.
"Two weeks ago: Judge refused bail to #JulianAssange saying that he, and all other prisoners, would be safe in Belmarsh Prison. Today the BBC is reporting first death in Belmarsh, with many other prisoners infected", the group wrote on Twitter.
Earlier in the day, Assange appeared before the court via a video link for a directions hearing.
The BBC broadcaster reported earlier in the day, citing internal documents, that a total of nine inmates in prisons across the country had died after contracting the virus. Among the fatalities was a Belmarsh prisoner.
Assange is currently awaiting a decision on whether he will be extradited to the US. The hearings, which began in February, were adjourned until May 18. If extradited to the US, the whistleblower will face up to 175 years in prison.