In updated guidance, it warns against all travel to Hubei province – where the virus began – and urged Britons already there to leave if they can.
The province has been on lockdown for days as the authorities try to contain the virus, which has so far killed at least 56 people.
But some British people in Hubei province say they cannot leave.
Home Secretary Priti Patel told Sky News that the government was “looking at all options” to help Britons in China, but would not confirm reports that plans were being drawn up to airlift people out.
The virus originated in the city of Wuhan in Hubei province, and has infected almost 2,000 people since its discovery.
In the UK, tests on 31 people suspected of contracting the virus have come back negative, the government said on Saturday.
In its most recent update, the Department of Health said there are currently “no confirmed cases in the UK or of UK citizens abroad, and the risk to the public is low”.
Officials are trying to trace around 2,000 people who have flown to the UK from Wuhan in the past fortnight.
Chinese President Xi Jinping has warned the spread of the virus is accelerating, telling senior officials the country is facing a “grave situation”.
Checkpoints in Hubei province are preventing people from leaving, the airport has been closed, and many of the roads are blocked to all vehicles except those carrying patients or medical supplies.
In addition, private vehicles have been completely banned from central districts of Wuhan.
British scientists have said that it may not be possible for China to contain the virus.
Researchers at the MRC Centre for Global Infectious Diseases have calculated that each person is passing the virus on to two or three others.
The scientists, based at Imperial College, London, say the transmission rate needs to be cut by 60% in order to get on top of the outbreak.
Some British citizens stranded in Wuhan have criticised the government’s response.
Yvonne Griffiths, a university lecturer from Cardiff, is due to fly home on Monday, but is not confident that will happen: “I am disappointed at the absolute silence on the issue of how stranded people are going to get home.
“And it seems maybe the British government at the moment has either a lack of concern or a lack of planning in place, I’m not sure.”
Sophie, from the UK, told BBC News that she and British housemate Jason had “been stuck in the house for four days”.
“We’re frustrated by the fact we don’t know what’s going on,” she said.
“It’s scary. We’ve heard the virus can stay in the system for two weeks without somebody showing signs they’re sick.”
She added it was now law that masks must be worn outside.
“There’s such a spotlight on us now. Our families are pretty worried.
“It’s a very uncertain time, we could be housebound for weeks. We don’t know whether to sit it out and wait, or try to leave the country.
On Saturday, Australia confirmed its first four cases – first in Melbourne, and then three more in Sydney.
It has also spread to Europe, with three cases confirmed in France.
China has flown specialist military medical teams into Hubei province and state newspaper the People’s Daily reported that a second emergency hospital was under construction, as the virus continues to spread.
Across mainland China, travellers are having their temperatures checked for signs of fever, and train stations have been shut in several cities. Many Lunar New Year celebrations have been cancelled.
From Monday, China is suspending all foreign trips by Chinese holiday tour groups, state media reported.
The US has announced that staff at the Wuhan consulate will be evacuated on a special flight on Tuesday.