Around 83 British nationals and 27 non-UK nationals landed at the Brize Norton RAF base in Oxfordshire at around 1.30pm on Friday, the Foreign and Commonwealth Office (FCO) said.
A convoy of six coaches arrived at Arrowe Park Hospital on the Wirral shortly after 7.15pm on Friday.
The vehicles were led by a police escort to the rear of the hospital and on to a side road leading to the accommodation block.
A medic wearing a white specialist suit was sitting next to the coach driver of each vehicle.
The Chief Medical officer confirmed on Friday morning that two patients in England have tested positive for the illness.
The pair are being treated by Newcastle upon Tyne Hospitals NHS Foundation Trust in its specialist Airborne High Consequences Infectious Disease Centre (HCID), Public Health England (PHE) confirmed on Friday.
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Health officials are urgently try to trace those who came into contact with two people diagnosed.
The UK passengers were taken to the Merseyside hospital to be housed in an NHS staff accommodation block with access to the internet.
Patients disembarked from behind barriers covering the accommodation entrance.
However, some could be seen inside wearing masks as they walked upstairs to their rooms for the next fortnight.
The quarantined people are being given fully-furnished rooms, food, laundry facilities and have access to a team of medical staff who will closely monitor their condition.
Kitchens are available for those who wish to self-cater, and families are being kept together, with games consoles, toys and cots also being provided.
Driver Liam Musgrove passed the convoy as it travelled up the M6 motorway.
“The experience was harrowing and quite surreal,” the 28-year-old told the PA news agency.
“Seeing such an organised operation in place it really puts into perspective what a deadly virus this could be.”
Chinese health officials said early on Saturday the death toll in the country from the virus had risen to 259, with the number of known cases rising from 9,962 to 11,791.
No deaths have occurred outside China, although cases have been confirmed across at least 23 countries.
The number of coronavirus cases worldwide has surpassed that of the SARS epidemic, although death rates are lower.