The patient began to feel unwell on the second evacuation flight carrying 11 British nationals from Wuhan to RAF Brize Norton in Oxfordshire.
The patient has been taken to hospital for coronavirus tests, while the other 10 continued their journey to join 83 others at Arrowe Park Hospital on the Wirral, according to an email from Janelle Holmes, chief executive of Arrowe Park.
All those who have returned from Hubei province in China are being quarantined in staff accommodation blocks on the site.
An internal email from Ms Holmes, revealed by the Liverpool Echo and also seen by the PA news agency, said the unwell passenger "immediately self-isolated" and was taken to a separate NHS hospital when the flight landed.
The email said: "Dear all, as you know, we were expecting a further 11 people, repatriated from Wuhan in China, to arrive and join you in the accommodation block at Arrowe Park Hospital last night.
"During the flight, one of the passengers started to feel slightly unwell, and self-isolated immediately.
"Upon landing, that passenger remains isolated, and was taken to another NHS hospital for tests.
"We expect test results in the coming days, and will keep you updated.
"None of the other 10 patients have shown any symptoms, but as a precautionary measure the 10 new guests were allocated rooms in a separate area of the facility, isolated from those already here.
"As we have previously said, staff supporting those in the accommodation block are following strict clinical guidance and protocols to ensure everyone remains safe."
It comes as the British Embassy in Beijing tweeted that the last flights from China to the UK for British nationals are set to leave this week.
It said flights will be run by "partner countries" and any British national and their immediate families, including those with non-UK passports, must make it known if they wish to travel.
"These may be the last flights for foreign nationals out of Hubei," the message said.
"If you are in Hubei and want to leave, please register with us as soon as possible using 24/7 contact numbers +86(0)1085296600 or +44(0)2070081500."
Separately, officials said there were no plans to introduce a US-style travel ban on foreign nationals who have recently been in China entering the country.
Sources told PA that the UK would continue to follow the advice of the World Health Organisation (WHO), which does not advocate such bans.
The Chinese government has accused the US of causing "panic" in its response instead of helping.
So far, more than 17,000 people in China have been confirmed with the virus and 361 people have died there.
In other countries, there are more than 150 confirmed cases and one person has died in the Philippines.
Health Secretary Matt Hancock is due to update MPs later when he makes a statement to the Commons.
Meanwhile, two people, a University of York student and one of their relatives, continue to be treated for coronavirus in the specialist infectious diseases unit at Newcastle Royal Victoria Infirmary.
Earlier on Monday, Mr Hancock announced that £20 million of UK Government funding is being put towards the development of a coronavirus vaccine.