The UK is “well prepared” to deal with coronavirus cases and the risk to individuals “remains low”, the government has said.
Downing Street said 99% of those tested in the UK had come back negative.
The total number of cases in the UK has risen to 13 after four cruise ship passengers flown back to Britain on Saturday tested positive for the virus.
It comes amid growing fears the outbreak could reach pandemic scale as more cases emerge around the world.
A total of 6,536 coronavirus tests have been conducted in the UK as of 14:00 GMT on Monday, with 6,527 returning as negative, the Department of Health said.
Italy has the largest number of coronavirus cases in Europe, currently 165, and has reported its fifth death from the virus.
It has taken tough measures to try and contain the outbreak, including enforcing a lockdown in several small towns in the Lombardy and Veneto regions.
Asked whether similar measures could be imposed in the UK, the prime minister’s official spokesman said: “We will be led by the advice from public health and medical experts and will take steps which they feel are required to best protect the British public.”
The risk to individuals “remains low” and 99% of those tested in the UK had come back negative, the spokesman added.
He said: “We are well prepared for UK cases, we are using tried and tested procedures to prevent further spread and the NHS is extremely well prepared and used to managing infections.”
The government will continue to “work closely” with the World Health Organisation and international partners, and “remain prepared for all eventualities”, he said.
The Foreign Office updated its travel advice for Italy over the weekend, the spokesman added.
Ireland’s Department of Foreign Affairs has advised its citizens not to travel to affected areas of Italy.
Meanwhile, rugby matches involving Welsh club Ospreys and Irish side Ulster have been postponed due to restrictions enforced by officials dealing with the outbreak in Italy.
Ospreys were due to play Zebre in Parma on Saturday, with Ulster set to face Benetton in Treviso later the same day.
Plans are being made to reschedule both fixtures.
The UK has supplied equipment including facemasks to China to help combat the spread of the disease, the spokesman confirmed.
“We have supplied [the Chinese government] with 1,800 goggles, 430,000 disposable gloves, 194,000 sanitising wipes, 37,500 medical gowns and 2,500 facemasks,” he said.
The total number of UK cases has risen to 13 after four cruise ship passengers flown to Britain on Saturday tested positive for the virus.
They were among 30 repatriated Britons and two Irish citizens beginning a 14-day quarantine at Arrowe Park Hospital in Wirral.
The four UK nationals caught the virus on the Diamond Princess liner in Japan and are being treated in specialist NHS infection centres.
Separately, four Britons from the ship who recently tested positive for the new coronavirus were not on Saturday’s repatriation flight.
They included David and Sally Abel, from Northamptonshire, who have since been diagnosed with pneumonia, according to their family and are being treated in a Japanese hospital.
The World Health Organization (WHO) has said it will not officially declare a coronavirus pandemic, but will start to use the term in communications if it reaches that stage.
Spokeswoman Margaret Harris said: “We could start describing it as a pandemic, but at the moment we are saying it is clusters and outbreaks in some countries.”
She said in most cases there was a clear epidemiological link between those affected and cases reported in Asia.
“If it became clear that it is all around the globe and we are seeing systematic community transmission, then we would say this meets the definition of a pandemic,” she added.
The statements come as nations including South Korea, Italy and Iran are battling to contain the virus, which causes respiratory disease Covid-19.
About 77,000 people in China, where the virus emerged last year, have been infected and nearly 2,600 have died.
More than 1,200 cases have been confirmed in about 30 other countries and there have been more than 20 deaths.