The first healthcare worker to die after contracting swine flu was not killed by the virus, Bedfordshire police said today.

Michael Day, 64, died at Luton and Dunstable hospital on Saturday. A postmortem examination found that the GP, from Bedfordshire, had died of natural causes, a police spokeswoman said.

The discovery means that only one person without underlying health problems has been confirmed to have died in the UK after contracting the H1N1 virus.

No inquest will be held into Day's death. Sources said he died from a blood clot to the lungs. He also suffered from heart disease and high blood pressure, and had viral pneumonia.

A postmortem examination on six-year-old Chloe Buckley, who died on Thursday at St Mary's hospital in Paddington, west London, is expected to take place this week and should establish whether she had underlying health problems. A council official described her last night as having been "perfectly healthy" a few days ago.

Earlier today, the health secretary, Andy Burnham, urged people to keep the threat posed by swine flu "in perspective" after the death of Chloe.

Burnham described her death as a tragedy but said many children had suffered from swine flu and gone on to make a full recovery.

"People do need to keep it in perspective – lots of children have already had swine flu and have made a very quick recovery and, obviously, in the early stages we saw lots of school closures," he told GMTV.

"There have been lots of children already having the condition but making a very quick and full recovery. We do have to keep it in perspective."

The health secretary said Britain was at the "front of the queue" for vaccine supplies and would start to receive the first next month.

"We have made very good plans in this country for this eventuality – for being in this situation," he said. "So as soon as stocks are made, the very first vaccines will come to this country."

The deaths of Chloe and Day took the number of people in the UK who have died after contracting swine flu to 17.

Chloe's parents, Michael and Jacinta, said in a statement released today that they were "satisfied that the medical care Chloe received at all times was appropriate" and criticised newspaper stories that suggested otherwise. Some reports said that she was misdiagnosed and not given anti-viral swine flu drugs when she first fell ill.

"We are obviously very distressed at the loss of our fun-loving baby girl," her parents said. "Nothing can replace her in our lives and we would plead with you to allow us to deal with our loss in private and without further intrusion."

The government has ordered enough swine flu vaccine to cover the entire population, with half of the doses expected by the end of the year.

A list has been drawn up of people who will be given the vaccine first, including health workers and patients with conditions such as diabetes and asthma.

At a meeting last night at St Catherine's school in West Drayton, where Chloe was a pupil, Daphne May, whose granddaughter is also a pupil, said there had been an air of panic.

"People are very worried and upset. We should have been told something sooner," said the 62-year-old. "Chloe was a beautiful girl, very polite, very petite, but we had heard that she had heart problems."

Chris Spencer, director of education and children's services at Hillingdon borough council, confirmed the school would close early for the summer break.

"It's an exceptional set of circumstances," he said. "This is a little girl who, until a few days ago, in all our minds was a child that was perfectly healthy so everybody here is in a deep state of shock and, with just a few days to go until the end of term, we've decided it's in the best interests of all involved."

Professor Steve Field, the chair of the Royal College of General Practitioners, said: "It is extremely important to remember that swine flu is currently a relatively mild condition in the majority of cases. The Royal College of General Practitioners has been working with the government on robust flu pandemic plans for a number of years and we are confident that the systems we have in place will cope well with the current pandemic."

Dr Laurence Buckman, the chair of the British Medical Association's GPs committee, said: "While these individual deaths are tragedies for the families concerned, it is very important that members of the public do not panic, and continue to follow health advice about swine flu and managing it if they are infected."