Health officials in the UK believe they have the strongest evidence yet that a new respiratory illness similar to the deadly Sars virus can spread from person to person.
Cases of the infection may come from contact with animals. However, if the virus can spread between people it poses a much more serious threat.
One man in the UK is thought to have caught the infection from his father.
However, officials say the threat to the whole population remains very low.
There have been 11 confirmed cases of the infection around the world. It causes pneumonia and sometimes kidney failure - five patients have died.
This is the third case identified in the UK. The first was a patient flown in from Qatar for treatment. The second was linked to travel to the Middle East and Pakistan.
The virus is then thought to have spread from the second patient to his son. There have been suggestions of person to person transmission in earlier cases in the Middle East, but this was not confirmed.
The third UK case is being treated in intensive care at the Queen Elizabeth Hospital in Birmingham.
The patient is known to have an underlying health condition which left them with a weakened immune system. This may have made them susceptible to the infection.
There have been no signs of the virus spreading to staff at the hospital.
Prof John Watson, head of the respiratory diseases department at the Health Protection Agency (HPA), said: "Confirmed novel coronavirus infection in a person without travel history to the Middle East suggests that person-to-person transmission has occurred, and that it occurred in the UK.
"Although this case provides strong evidence for person to person transmission, the risk of infection in most circumstances is still considered to be very low."
The exact source of the new virus and how it spreads is still unknown. The leading theory is that it comes from animals, the new Sars-like virus does appear to be closely related to a virus in bats.
However, if the infection needs to jump from an animal to a person with each infection the threat would be much lower.
The World Health Organization reported cases from within the same family in Saudi Arabia in November 2012.
It was impossible to tell whether each patient caught the infection separately - or if it had spread between them.
A WHO spokesperson said: "We know that in some of those cases there was close physical contact between family members caring for one another, so we can't rule out human-to-human transmission."
The two cases in the UK, with only one case linked to foreign travel, provide the strongest evidence that the infection can spread between people. The Health Protection Agency (HPA) said it was "overwhelmingly likely" human-to-human transmission had occurred.
However, if the virus could readily and easily spread between people then far more cases than the 11 detected so far would have been detected.
Coronaviruses are a large family of viruses ranging from the common cold to the Sars (severe acute respiratory syndrome) virus, which spread through droplets of body fluids produced by sneezing and coughing.
It is thought these cases do not represent a "tip of the iceberg" with far more people being infected with mild or no symptoms, but the infection is still being analysed.
In 2003 an outbreak of Sars killed about 800 people after the virus spread to more than 30 countries around the world.
The new coronavirus was first identified in September 2012 in a patient in Saudi Arabia who has since died.
No travel restrictions are in place.
Prof John Oxford, a virology expert at Queen Mary, University of London, said: "This doesn't raise too many alarm bells.
"In a family things can spread far more easily than they would spread outside, people share towels and toothbrushes etc.
"If it was somebody who was not related or a nurse or a doctor - that would be a lot more serious."
Prof Ian Jones, from the University of Reading, said: "There is really close contact involved here, it is not 'true' human transmission in the general public.
"Although it is severe, it's not doing anything worse than some other respiratory infections, it's just a new one."
Prof Wendy Barclay, from Imperial College London, said it was wise to keep a close eye on the virus.
"We're an incremental step closer to worrying, but it isn't a worry where we need to say there is a pandemic coming," she said.