Coronavirus: Signs the new Sars-like virus can spread between people
Cases of the infection come from contact with animals, however, if the virus can spread between people it poses a much more serious threat.
One person in the UK is though to have caught the infection from a relative.
However, officials say the threat to the whole population remains very low.
There have been 11 confirmed cases of the infection around the world, 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 a close relative. 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 may have made them susceptible to the infection.
Prof John Watson, head of the respiratory diseases department at the Health Protection Agency, 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."