Australia, Japan, the US, and EU nations are also repatriating citizens.
BBC health editor Hugh Pym said that Health Secretary Matt Hancock has instructed officials to put them in quarantine for two weeks – possibly at a UK military facility.
Sources told the BBC the returning Britons will be given the best possible medical care and advice.
Those returning from other parts of China will not be affected, but have been advised to “self-isolate” for 14 days.
Australia plans to quarantine it’s 600 returning citizens for two weeks on Christmas Island – some 2,000km (1,200 miles) from the mainland.
British Airways, which operates daily flights to Shanghai and Beijing from Heathrow, announced the suspension of flights to and from mainland China “with immediate effect” until 31 January while it assesses the situation.
A statement said: “We apologize to customers for the inconvenience, but the safety of our customers and crew is always our priority.”
Other airlines, including United Airlines, Air Canada and Cathay Pacific Airways, have already canceled some flights to China.
What’s happening to people stuck in Wuhan?
Some Britons in Wuhan said they had not been told about the quarantine plan, with one man having refused his place on the flight for fear of spreading the disease.
Kharn Lambert told the BBC’s Victoria Derbyshire program that the embassy said it is their own responsibility to arrange transport home and isolate themselves.
“I don’t want to put the health of regular, everyday British citizens at risk,” he said.
British lecturer Yvonne Griffiths, who is currently in a hotel in Wuhan, said she was told in the early hours of Wednesday morning that there would be a flight from Wuhan airport to the UK.
“We have to be there six to seven hours before the flight leaves, and we would have screening from some health people here in Wuhan, and if we are not showing any symptoms then we’ll be able to board that plane,” she said.
“If we were to be suffering temperature or any other symptoms, breathing problems, then there seems to be a possibility of quarantining at this end.”
Another British man, Jeff Siddle, from Northumberland, said that he and his daughter had been offered seats on a flight on Thursday – but not his wife, who’s a Chinese national. China is not allowing its citizens to leave the country.
What’s the latest on the virus itself?
The number of deaths from the virus has risen to 132 in China, the Chinese National Health Commission (NHC) said on Wednesday.
Four cases have been confirmed in Germany, making it the second European country to report cases, after France.
The United Arab Emirates has also confirmed its first cases of the virus in a family who recently returned to the UAE from Wuhan.
Coronavirus in China
- 5,974Confirmed cases
- 9,239Suspected cases
- 16Other countries with confirmed cases
An expert from the NHC said it could take 10 more days for the outbreak to the peak.
Like similar Sars and influenza viruses, the new coronavirus is a particular risk for elderly people and those with pre-existing illnesses.
The sharp rise in cases is in part attributed to increased awareness, monitoring, and testing in recent days.
One theory is that the virus, which can cause severe acute respiratory infection, may have emerged from illegally traded wildlife at a seafood market in Wuhan, the capital of Hubei province.
There is no specific cure or vaccine. A number of people, however, have recovered after treatment.
Which other airlines are suspending flights?
United Airlines has canceled 24 US flights to Beijing, Hong Kong and Shanghai between 1 and 8 February because of a sharp drop in demand.
Cathay Pacific said it would cut flights to China from 30 January to the end of March, while Air Canada has also reduced its number of flights.
Indonesia’s Lion Air said it would be temporarily suspending flights from Saturday, affecting dozens of flights on routes to 15 Chinese cities.
Russia’s Ural Airlines said it had suspended some services to Europe popular with Chinese tourists, including Paris and Rome, because of the outbreak.
Other airlines are introducing measures aimed at reducing the chances of spreading the virus.
Taiwan’s China Airlines said it was encouraging passengers to bring their own beverage bottles, while Singapore Airlines was among those allowing the crew to wear masks on China flights.
Who else is being evacuated?
New Zealand will cooperate with Canberra to bring its 53 citizens home alongside the Australian evacuees.
Some 200 Japanese nationals have been flown from Wuhan and have landed at Tokyo’s Haneda airport.
Around 650 others said they wanted to be repatriated, and the Japanese government said new flights were being planned.
According to Japanese media, several of the returnees were suffering from fever or coughs. All will be taken to the hospital, regardless of whether they are showing symptoms.
Also on Wednesday, 240 Americans – including workers the local US consulate – left the city.
According to CNN, the evacuees might have to stay in isolation in an airport hangar for up to two weeks.
Separately, two aircraft to fly EU citizens home were scheduled, with 250 French nationals leaving on the first flight.
South Korea said some 700 of its citizens would leave on four flights this week. Both Malaysia and the Philippines also said they would evacuate their citizens in and around Wuhan.
Meanwhile, Hong Kong announced plans to slash cross-border travel between the city and mainland China.