Medical staff and patients at a hospital in Milton Keynes have been placed in isolation after a man in his 80s became the second person in Britain to have died from coronavirus, amid family fears he was not isolated quickly enough.

Milton Keynes University Hospital NHS Foundation trust said the man, who had recently returned from a Caribbean cruise, tested positive for coronavirus shortly before his death on Thursday.

The chief medical officer, Prof Chris Whitty, said: “I am very sorry to report a second patient in England who tested positive for Covid-19 has sadly died. I offer my sincere condolences to their family and friends and ask that their request for privacy is respected.

“The patient, who was being treated at the Milton Keynes University Hospital, was an older patient who had underlying health conditions. Contact tracing is already underway.”

The fact that staff were forced into isolation will raise concerns about the effect of Covid-19 on hospitals’ ability to cope with the outbreak.

A family member, who did not wish to be named, told the Guardian: “Our concern is that the hospital were too slow to detect that our relative had symptoms similar to those of coronavirus and too slow to move him from a ward into isolation, and that that may have put a lot of people – fellow patients on the ward, staff who were looking after him and visitors who came to see him – at risk of contracting the virus from him.

“We think they should have put him into isolation right away, as soon as he arrived, given his symptoms. That was a failure by the hospital. He was coughing a lot and had quite severe symptoms.

“Despite that, he was put on a ward with lots of other sick patients for six or seven hours before he was moved into isolation. During that time a lot of relatives came to see him, both adults and children. Who knows if any of them have now got coronavirus and are maybe spreading it to older people who might get sick?”

They said that the family were told at around 7pm on Thursday that their relative had coronavirus – and about an hour later were told he had died. They said the family were also concerned about the reason they were given for his death, which was presumed to be that he took off his oxygen mask and asphyxiated. NHS England was approached for comment about the death of the patient.

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On Wednesday, King’s College London confirmed that an immunobiology student working in an asthma and allergy research department at Guy’s hospital in London had tested positive and several other staff had been advised by NHS England to self-isolate.

In other developments on Friday:

The Department of Health announced the biggest increase in the number of people infected, which jumped by 4 to 164. Two British Airways baggage handlers were among those who tested positive.

A £46m fund was announced by the government in an effort to find a vaccine and speed up testing.

Public Health England said “social distancing” measures such as avoiding cinemas, pubs or sporting events might be needed in the future.

At least 142 Britons are among more than 2,000 passengers and crew quarantined on a cruise ship off the coast of California because of fears they may have been exposed to the coronavirus.

The prime minister, Boris Johnson said on Friday: “It looks to me as though there will be a substantial period of disruption when we have to deal with this outbreak.

“How big that will be, how long that will be, I think, is still an open question.

“But, clearly, it is something we are going to have to deal with for quite a while in the UK.”

More deaths would occur in Britain, experts said. Prof George Lomonossoff, of the John Innes Centre in Norwich, said: “It’s very sad, but I think it is inevitable that we will see further deaths in the next few days and weeks. Likewise the number of cases is probably going to rise fairly quickly in that same period.

“We are now entering the phase where transmission between people who have not travelled to infected areas will become dominant.”

The role of the British Airways workers will raise concerns about the possibility they may have inadvertently spread the disease through surface contact.

It is possible to pick up the virus on your hands from a surface that somebody with the infection has touched, although it is more likely to be transmitted by other means. The virus can linger for 48 hours or even possibly 72 hours on a hard surface, which is why emphasis is placed on handwashing.

The travel industry has already been hit hard by the coronavirus outbreak. The contagion proved the last straw for the Exeter-based airline Flybe, which collapsed into administration on Thursday. On Wednesday, the German airline Lufthansa grounded 150 planes amid low demand.

Officials from the Department for International Development hope the £46m pledged will help in the development of the eight possible coronavirus vaccines being worked on by scientists.

A rapid diagnostic test could also be used by low-income countries around the world that are not currently able to diagnose the virus at all.

No one was has been allowed to leave the Grand Princess cruise ship, which was stuck off the coast of San Francisco, with guests being confined to their rooms pending test results. Meals were delivered to passengers’ cabins and they were given free internet access and extra films to watch on the onboard televisions, Princess Cruises said.

Last week, a passenger on its sister ship, the Diamond Princess, which was quarantined in Japan, became the first UK citizen to die from the virus.