Someone died within the Leeds Teaching Hospitals NHS Trust on Wednesday, September 9, the latest figures from NHS England show.
Fourteen deaths from coronavirus have been registered across England today, bringing the total number of confirmed reported deaths in hospitals to 29,676.
Patients were aged between 62 and 94 and all had known underlying health conditions.
There were two other deaths in Yorkshire hospitals - one person died at Sheffield Teaching Hospitals NHS Foundation Trust on Sunday, September 13 and one person died at Calderdale and Huddersfield NHS Foundation Trust on Saturday, September 12.
It comes as Health Secretary Matt Hancock told MPs suspected Covid-19 patients with acute medical needs and people in care homes will be prioritised under plans to ration coronavirus tests.
NHS leaders have called for health workers and patients to be given priority after Government sources admitted that demand for tests is currently far outstripping supply.
The Health Secretary acknowledged that there were “operational challenges” in the testing system as he was summoned to answer an urgent question on the situation in the Commons.
Mr Hancock said an updated prioritisation list would be published setting out who will be at the front of the queue for tests.
It comes after anyone suffering symptoms, regardless of where they work or live, were urged to book tests in recent months.
“We have seen a sharp rise in people coming forward for a test, including those who are not eligible,” Mr Hancock said.
“Throughout this pandemic, we have prioritised testing according to need. Over the summer, when demand was low, we were able to meet all requirements for testing, whether priorities or not.
“But as demand has risen, so we are having to prioritise once again and I do not shirk from decisions about prioritisation. They are not always comfortable, but they are important.”
Acute clinical care is the top priority, with social care next on the list and currently receiving more than 100,000 tests a day.
Mr Hancock said prioritisation was “a choice that we must make”.
Government sources acknowledged there was no accurate data on how many people who are not eligible for a test have tried to book one.
They said that, overall, the gap between members of the public seeking a test and being able to do a test “is not going to go away.”
Shadow health secretary Jonathan Ashworth told MPs that Mr Hancock was “losing control of this virus”.
Mr Hancock acknowledged that it might be “a matter of weeks” before the problems are resolved.
There have been widespread complaints that tests are unavailable, people are waiting more than 24 hours for results, or are being forced to travel long distances to get a test.
But Mr Hancock told MPs that the average distance travelled to a test site is now 5.8 miles, down from 6.4 miles last week.
He told the Commons: “Everyone in this House knows that we’re doing more testing per head of population than almost any other major nation, and I can update the House that we have now carried out over 20 million tests for coronavirus in this country.
“As we expand capacity further, we’re working around the clock to make sure everyone who needs a test can get a test.”
But he acknowledged the virus was spreading, both in the UK and around the world.
Figures on Monday showed 2,621 confirmed new cases and “the epidemic is growing”, Mr Hancock said.
“There are signs that the number of cases in care homes and the number of hospitalisations is starting to rise again,” he said, explaining why the “rule of six” restrictions were imposed on Monday.
Downing Street denied reports that tests are not available in the worst-hit parts of England.
A No 10 spokesman said: “We would say that it is wrong to say that testing is not available in these areas.
“Our capacity continues to be targeted to where it is most needed, which is why booking slots and home testing kits are made available daily for people with symptoms.”
The testing situation was discussed at the Cabinet meeting on Tuesday.
Experts had called for tests to be rationed, and complained that capacity had not expanded to meet the expected rise in demand as schools reopened and people returned to workplaces – as the Government has urged in England.
Sir John Bell, regius professor of medicine at Oxford University, who has been advising ministers, said the speed at which more people would need tests had been underestimated and warned that the problem could get worse.
Sir John told BBC Radio 4’s Today programme: “I think what’s going wrong is the second wave.
“A month ago, they had spare capacity in testing, significant spare capacity, but I think what has been underestimated was the speed at which the second wave would arrive, but also the pressure put on the system from children returning to school, and the testing demands associated with that, and people increasingly out and about.
“So I think they are definitely behind the curve in terms of getting the necessary tests for what we need today.”
NHS Providers chief executive Chris Hopson said the health service in England had been hit by staff being off work who were unable to get a test.
He said the NHS “simply can’t spare members of staff waiting for tests not being able to come into work” and patients unable to be tested.
Professor Alan McNally, director of the Institute of Microbiology and Infection at the University of Birmingham, who helped set up the Milton Keynes Lighthouse Lab, told BBC Breakfast there were “clearly underlying issues which nobody wants to tell us about”, plus a surge in demand for tests.
A Government source said that while hospital admissions for Covid-19 are currently at a low level, they will rise as infections rise across the community.
They said that whereas younger people were most affected in recent weeks, this has now translated into older age groups catching the virus.
As a result of rising cases, the country could be in for a tough six months, they added.