The Health Protection Agency (HPA) said the man had been in close contact with a relative who had picked up the infection while travelling in the Middle East and Pakistan.
The so-called "novel" coronavirus causes severe breathing problems and has killed five of the 11 confirmed cases around the world.
The HPA announced on Monday the first case in a UK resident, and said the critically ill man was being treated in isolation at the Wythenshawe Hospital in Manchester.
A third case involves a man from Qatar who is receiving treatment in the UK.
The new case is receiving intensive care at The Queen Elizabeth Hospital in Birmingham. It is understood that he has an existing medical condition that may have made him more susceptible to respiratory infections.
Professor John Watson, head of the respiratory diseases department at the 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.
"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."
Coronaviruses can cause the common cold, but can also result in more severe illness such as Sars (Severe Acute Respiratory Syndrome).
Anyone who develops a fever, cough, and breathing difficulties within 10 days of travelling to the Arabian peninsula or surrounding countries should seek medical advice and mention their travel itinerary.
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