Two further patients in England have tested positive for coronavirus, bringing the total number of UK cases to 15, according to the Department of Health.
The virus was passed on to one patient in Italy and to the other in Tenerife.
A school and a GP surgery in Buxton, Derbyshire, have been shut down due to one of the new cases.
Burbage Primary School told Sky News the school was closed because a parent had tested positive.
Meanwhile, Buxton Medical Practice urged people not to go to the practice on Thursday due to a confirmed case of coronavirus.
The patients have been transferred to specialist NHS infection centres in Royal Liverpool Hospital and the Royal Free Hospital, London.
The latest UK cases emerged as European countries struggled to contain the virus.
Update on #coronavirus:— Department of Health and Social Care (@DHSCgovuk) February 27, 2020
Two further patients in England have tested positive for #COVID19, bringing the total number of UK cases to 15.
Patients have been transferred to specialist NHS infection centres.
Italy has confirmed at least 400 cases and 12 deaths after a severe outbreak in the north of the country.
Austria, Croatia and Switzerland also reported their first cases linked to the outbreak in Italy, while Spain and France recorded new ones, also involving people who had been to northern Italy.
France recorded its second death on Wednesday, a 60-year-old Frenchman who died in a Paris hospital.
Dr Tom Wingfield, senior clinical lecturer at Liverpool School of Tropical Medicine, said: “The new patients diagnosed today in the UK and now being managed in specialist infection units in Liverpool and London are not surprising and do not change the understanding of what the outbreak will look like in the UK.
“There are likely to be some more cases in the coming weeks but the UK public can be reassured that we have experienced teams in place to manage the isolation and care of people diagnosed with coronavirus and perform robust tracing and screening of their contacts.”
Some 168 Britons have been told to isolate themselves at the H10 Costa Adeje Palace in Tenerife after a three tourists staying there tested positive.
Footage shared by a British guest on Wednesday showed tourists strolling through the hotel grounds and swimming in the pool without masks, despite instructions to stay inside their hotel rooms.
Travellers returning to the UK from northern Italy were told they may need to self-isolate as part of measures to stop the spread of illness.
Schools and businesses have been urged not to overreact as the coronavirus continues to spread.
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At least eight schools in the UK have closed while others – including Prince George’s – have sent pupils home amid fears they may have been exposed to coronavirus during trips to northern Italy.
However, Public Health England (PHE) said that its general advice is not to close schools – a message echoed by health secretary Matt Hancock.
Businesses have been advised that employees do not need to wear face masks, as the government looks to combat panic over the illness.
Guidance published by ministers says face masks are only recommended to be worn by “symptomatic individuals” to reduce the risk of transmitting the infection to other people.
The Business Department and PHE recommended that the best way to reduce any risk of infection is good hygiene and avoiding direct or close contact (closer than two metres) with any potentially infected person.