Britain's Health Protection Agency (HPA) said the latest person to contract novel coronavirus was a relative of two other cases announced earlier this week, who were admitted to intensive care wards at two British hospitals.
The first member of the family, who was confirmed on Monday as having the virus, had recently travelled to the Middle East and Pakistan. Their two relatives had no recent travel history.
Five people have died of the virus, according to the HPA -- three in Saudi Arabia and two in Jordan.
The HPA said the latest patient was "recovering from a mild respiratory illness and is currently well".
John Watson, head of the HPA's respiratory diseases department, said the agency was in contact with people who had been in contact with the family.
He stressed that the risk of infection remained low.
"If novel coronavirus were more infectious, we would have expected to have seen a larger number of cases than we have seen since the first case was reported three months ago," he said.
Coronaviruses cause most common colds but can also cause SARS (severe acute respiratory syndrome).
A SARS epidemic killed more than 800 people when it swept out of China in 2003, sparking a major international health scare.