It comes as a man in the Philippines became the first person to die from the virus outside China.
The second group of British evacuees boarded a French flight and will also be brought to Arrowe Park Hospital in the Wirral where they will spend 14 days in quarantine, Foreign Secretary Dominic Raab said.
He told Sky's Sophy Ridge On Sunday: "It's correct that there is a further French flight that is expected back in Europe today and that will carry some UK nationals."
Mr Raab later confirmed 11 British nationals would be returning and said the Government is doing all it can to help Britons in Wuhan leave if they want to.
Appearing on the BBC's Andrew Marr Show, he said: "We'll do everything we can to make sure that those that still want to leave, give them the opportunity to do so," he said.
He added: "The challenge that we've got, and the Chinese have got frankly, is to contain the virus but also then to lift out people that want to come back home and we're doing that as sensitively and as effectively as we can."
The latest repatriation comes as the Government launched a public health campaign advising people how to slow the spread of the virus.
A University of York student and their relative remain the only two confirmed cases in the UK.
From Sunday, advertisements advising people to use tissues when sneezing or coughing and wash their hands regularly will appear in newspapers, on the radio and on social media.
The ads will also target publications and forums in the UK known to be read by Chinese nationals here, the Department of Health said.
Health Secretary Matt Hancock said UK medics are working "round the clock" to prevent the spread of the illness, but added the general public can do its bit.
He said: "Basic hygiene such as washing our hands regularly and using tissues when we cough and sneeze can play an important role in minimising the spread of viruses like this."
The Foreign Office, which has withdrawn some staff from China and closed the British Consulate-General in Wuhan, said it is continuing to work with EU countries to add remaining Britons to any rescue flights they may charter back from Wuhan.
A spokesman for the Foreign Office (FCO) said: "The Government is in touch with British nationals who remain in Wuhan, and are doing everything we can to bring them home as safely and quickly as possible."
The death toll has risen above 300 and the number of confirmed cases of infection increased to 14,380, Chinese authorities said.
Some of the 83 Britons holed up quarantine in the Wirral shared video footage of their first hours in a locked NHS staff accommodation block following their arrival back in the UK on Friday's evacuation flight.
They showed the food and other essential items they had been provided with, and referenced entertainment including televisions and Playstations - which will help them while away their 14 days in isolation.
The University of York's vice-chancellor, professor Charlie Jeffery, acknowledged the "concern and anxiety" among students and staff when details of one of the UK's two cases were confirmed.
But the university said the wider risk remains low as investigations revealed the unnamed student has not been on campus since being exposed to the virus, and was not there in the period beforehand either.
Public Health England is continuing to work to try to trace people who had close contact - defined as being within two metres of the infected person for 15 minutes - with the pair, who had checked in to the Staycity apartment-hotel in York and are now being treated at a specialist unit in Newcastle.
One expert called on health bosses co-ordinating the response to the virus to share more information about any future cases sooner in order to reassure people.
Professor Paul Hunter, from the University of East Anglia, said the York location and dates on which people might have come into contact with the two confirmed cases could have been provided so people knew whether they were at risk or not.
The university has advised people concerned about their health in relation to the disease to call 111, and have also set up a call centre over the weekend.
The UK risk level from coronavirus remains at moderate, having been raised from low last week, on the same day the World Health Organisation (WHO) declared an international public health emergency.
The number of coronavirus cases worldwide has surpassed that of the Sars epidemic, although death rates are lower.
Many other countries have said they plan to quarantine evacuees for two weeks to avoid spread of the virus.
Evacuation flights by European governments out of Wuhan - where the virus was first identified - are expected to continue.
Russia, Mongolia and North Korea have announced that