The chief medical officer has confirmed the second person to die after contracting coronavirus is a man in his early 80s.
The man was understood to have underlying health conditions and died at Milton Keynes Hospital.
Test results confirmed he had COVID-19.
"I am very sorry to report a second patient in England who tested positive for COVID-19 has sadly died," professor Chris Whitty said.
He added: "I offer my sincere condolences to their family and friends and ask that their request for privacy is respected."
Professor Whitty said contact tracing was under way to find anyone who came into contact with him in the days before his death.
Hospital staff who nursed the patient have gone into isolation.
Milton Keynes University Hospital NHS Foundation Trust confirmed the man died shortly after testing positive for the virus.
The trust said all services and appointments at the hospital were "running normally" and that it was following advice to minimise the risk of the virus spreading.
Forty-eight new coronavirus cases have been confirmed in the UK over the past 24 hours, taking the total to 164.
On Thursday, a woman reported to be in her 70s became the first person in the UK to die after being diagnosed with coronavirus.
The Royal Berkshire Hospital in Reading said the woman had been "in and out of hospital" for other reasons but was admitted on Wednesday evening and tested positive.
Meanwhile, two British Airways staff, believed to be baggage handlers, tested positive for coronavirus on Friday and are recovering at home in isolation.
Also, Facebook is closing its London offices until Monday and telling staff to work from home after an employee was diagnosed with COVID-19.
The employee who was diagnosed with the virus was normally based in Singapore, the company told Sky News, but had visited the London offices between 24-26 February.
The UK's deputy chief medical officer Jenny Harries told Sky News: "The UK has planned for pandemic flu for many many years, and the NHS can flex its system up and down to manage large numbers of cases.
"That's exactly what we'll do here."
She added: "It's important at any time of year, particularly in winter, that if you have elderly relatives and are particularly unwell yourselves, you should avoid visiting them."
The government is working with supermarkets to ensure food supplies as the number of people self-isolating with the virus continues to rise, Health Secretary Matt Hancock said.
He sought to reassure the public following panic-buying in some areas, saying the government is "working to makes sure that if people are self isolating, they will be able to get the food and supplies that they need".
He added there was "absolutely no need" for individuals "to go round buying more than they need."
Health chiefs said people diagnosed with coronavirus who show only "very minimal" symptoms should self-isolate at home rather than in hospital.
Travellers returning to the UK from anywhere in Italy have also been advised to self-isolate if they develop symptoms.
In other developments:
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