The announcement comes after more than 80 Britons on an evacuation flight from the Chinese city at the centre of the outbreak were due to land in the UK.
In a statement, Professor Chris Whitty, said: "We can confirm that two patients in England, who are members of the same family, have tested positive for coronavirus". However, it is understood they are not in the Wirral area, where a special facility has been set up to quarantine those returning from Wuhan.
Health officials in Britain said on Friday that two people had tested positive for the novel coronavirus, the first confirmed cases in the country since the deadly outbreak began in China.
At least 213 people in the China have died from the virus, mostly in Hubei, with nearly 10,000 cases nationally.
"We are continuing to work closely with the World Health Organisation and the worldwide community as the outbreak in China develops to ensure we are ready for all eventualities".
Ghebreyesus praised China's speed on detected the outbreak, isolating the virus, sequencing the genome and sharing it with the World Health Organization, saying the country's efforts were "very impressive". No deaths have been reported outside China.
The virus has already spread to 18 other countries outside China.
He added: "Our greatest concern is the potential for the virus to spread to countries with weaker health systems, and which are ill-prepared to deal with it".