Coronaviruses are causes of the common cold but can also include more severe illness, such as Severe Acute Respiratory Syndrome.
This new coronavirus was first identified last September in a patient who died from a severe respiratory infection in June 2012.
"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 United Kingdom," John Watson, head of the respiratory diseases department at the HPA, said in a statement.
"This case is a family member who was in close personal contact with the earlier case and who may have been at greater risk of acquiring an infection because of their underlying health condition."
To date, evidence of person-to-person transmission has been limited. 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, Watson said.
"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," Watson said.
HPA said to date there have been 11 laboratory confirmed cases: five in Saudi Arabia with three deaths, two in Jordan and both died, one case in Germany who recovered and three in the Britain -- one patient from Qatar and two British patients currently receiving treatment in England.