- Video report by ITV News Asia Correspondent Debi Edward
It comes as more than 100 people have now died in the country, with confirmed infections surging to more than 4,500.
The British embassy in Beijing has said transport to get UK citizens out "may happen quickly and with short notice".
Meanwhile a chartered plane sent to China to pick up Americans in the city of Wuhan has departed and is en route to the States, according to a U.S official.
The UK government are yet to confirm repatriation details, but a teacher in Wuhan city said UK citizens were being given details of forthcoming flights.
- Asia Correspondent Debi Edward explains what the FCO warning means for Britons currently living or staying in China
The FCO updated its travel advice to urge UK citizens to avoid the country, adding it may become more difficult for British nationals in other provinces to leave.
The Foreign Office added UK nationals in China should "make decisions based on their own personal circumstances" over whether to leave.
Foreign Secretary Dominic Raab said: "Due to the increasing travel restrictions and the public health situation, we now advise against all but essential travel to China.
"We are also working urgently to finalise arrangements for an assisted departure from Hubei Province for British nationals this week, and are in contact with people in Hubei to ensure they register their interest and that we can keep them updated.
"The UK continues to be guided by the latest medical advice about the coronavirus outbreak. The safety and security of British people will always be our top priority."
The British teacher living in Wuhan, who asked not to be named, said she had been in contact with the British authorities who informed her that while she could return to the UK, her husband, who has a UK visa, would not be allowed to as he is a Chinese national.
It is understood this was a result of restrictions imposed by China, rather than the UK.
As a result, she decided that she would remain in China with her husband.
She said: "It’s what we were expecting to be honest, as we’d heard that it was like that for the American flight out.
"We had hoped it would be different, but oh well."
"If the situation stays as it is, or improves, then we’re fine. We just hope it won’t get any more serious," she said.
She adds that a number of other Britons she was in contact with had arranged to return home, with some scheduled on a flight at 7am on Thursday.
The news comes as almost 100 people in the UK have tested negative for coronavirus.
Video footage captured in Wuhan by resident Lin Wenhua shows a city shut off from the outside world, as he travels through empty streets of the city.
Mr Lin said people in the city at the centre of the outbreak are "fearful and anxious" but people "are facing the situation in a positive way".
The Department of Health and Social Care said 97 people have been given the all-clear for the virus, although scientists predict it may have entered the country.
Officials estimate up to 200 citizens currently there will want to return to the UK.
Hubei province has been on lockdown for several days as China seeks to contain the illness, as have other parts of China.