Those on board the vessel, which is docked off the coast of Yokohama, are anxiously waiting news on when they will be flown home.
Japanese authorities have now allowed passengers to disembark the ship but have been told those who do may not be able to join a planned evacuation flight.
The Foreign and Commonwealth Office (FCO) said it is planning a chartered flight from Tokyo for “as soon as possible”.
“We hope the flight will be later this week, subject to permissions from the Japanese authorities,” a spokesman said on Tuesday night.
"We have the utmost concern for the affected Britons and strongly encourage them to register for the evacuation flight."
The FCO has faced pressure to fly home the 74 Britons on board after the US chartered two planes for its citizens.
Brits David Abel and his wife Sally, who were also isolated on the vessel, said they were among 88 others confirmed to have become infected with the virus.
The couple have been posting regular Facebook updates and pleaded with the UK government to be flown home.
Mr Abel, 74, said they had tested positive and also claimed the Japanese authorities were taking them off the ship to a “hostel” rather than a hospital.
Two Irish passengers who were on board the cruise ship have also been diagnosed with the deadly illness.
Simon Coveney, Ireland’s deputy prime minister, said: “Two of these tested positive for Covid-19 and are currently being treated in hospital in Japan.
“These citizens share dual citizenship with another EU member state and are not normally resident in Ireland.
“Our Embassy in Tokyo is in ongoing contact with them regarding their consular needs.”
The Diamond Princess has been moored off the coast of Yokohama, near Tokyo, since February 3.
A total of 542 people on board testing positive for the respiratory illness, known as Covis-19.
Elsewhere, Britons are being tested for coronavirus in Cambodia after leaving a cruise ship where an elderly woman was diagnosed with the illness.
Passengers disembarked from the Holland America Westerdam ship on Friday, and hundreds have undergone testing for the virus.
It is unclear how many Britons were on board, but the Foreign Office said it is in contact with British nationals in Cambodia who were on the ship.
The Westerdam cruise liner remains in Sihanoukville, Cambodia.