The plane is expected to leave in the early hours of Sunday morning local time and will land at RAF Brize Norton, the Foreign Office said - adding that they want to ensure that all British nationals in Hubei province contact their team to register if they want to leave on the flight.
It is understood 165 Britons and their dependants remain in Hubei province, the epicentre of the outbreak, while 108 people have requested assistance to leave as of the early hours of Wednesday.
A total of 94 UK nationals and family members have already been evacuated to Britain from Wuhan on two flights which arrived on Friday and Sunday.
One passenger was taken to hospital in Oxford after telling medics he had a cough and a cold, while the rest of those who came back are in quarantine at Arrowe Park Hospital on the Wirral.
Foreign Secretary Dominic Raab said on Tuesday night: "We have been working round the clock to help British nationals leave Hubei province, on UK, French and New Zealand flights.
"The Foreign Office is chartering a second and final UK flight with space to help all British nationals and their dependants remaining in Hubei to leave.
"I encourage all British nationals in Hubei to register with our teams if they want to leave on this flight."
Meanwhile, 14 Britons and dependants left Wuhan for Auckland in New Zealand on Tuesday evening - with a British diplomat thanking her Kiwi counterparts for holding up the plane to allow a four-year-old to get clearance to fly.
Danae Dholakia tweeted: "So grateful to #NZ colleagues for getting 14 Brits/family members onto NZ flight from Wuhan last night, incl. holding up departure so @ukinchina could get clearances for the last passenger, a British 4 yr old child, to board. New Zealand: you're wonderful!"
The death toll from the coronavirus outbreak continues to rise with Chinese authorities reporting 490 victims and an increase in the number of cases to 24,324.
In Japan, 10 people on the Diamond Princess cruise ship tested positive for the virus and were being taken to hospitals, while 3,700 other passengers will be quarantined on board.
Among those stuck on the ship in Yokohama Bay, near Tokyo, are David and Sally Abel.
Speaking on a video posted on Facebook, Mr Abel, of Woodford Halse in Oxfordshire, said: "It appears that our quarantine is on board the ship, that we will not be taken off to a hospital.
"The 10 people that are affected, they are being taken off very soon by the local coastguard into a medical facility. We are to remain on board the ship and we are confined to our cabins.
"Naturally, we want to be home. We are missing our little Yorkie dogs. But two weeks, it'll go quite quickly I hope."
In an interview with the Press Association on Tuesday, a British man who fears he contracted coronavirus said he is isolated in his apartment in Wuhan and has been given no indication of when he will be able to leave the city.
Jamie Morris, a 23-year-old teacher from New Tredegar in South Wales, said he believes he may have contracted the virus at the end of November, before the mass outbreak prompted global media attention.
He said he had not been able to make the recent flights back to the UK because his passport had been given to the Chinese government to extend his residency permit.
He said the Foreign Office's crisis team in London had told him "to be patient and they will be in touch if anything changes".
Earlier, Mr Raab said: "We now advise British nationals in China to leave the country if they can, to minimise their risk of exposure to the virus.
Health Secretary Matt Hancock said on Monday there were "no plans to evacuate all remaining UK nationals in China".
He added: "We haven't seen the peak of the coronavirus by a long stretch and we expect more cases in the UK.
"We have a full plan in place to treat all those who have symptoms and test positively for coronavirus and we are working with international partners both to slow the spread and also to do the research that we need to do to find a vaccine."
Health officials are trying to trace 239 people who flew from Wuhan to the UK before travel restrictions came into force.
The Department of Health said that, as of Tuesday, 414 people have tested negative for coronavirus.
The World Health Organisation said it is still early in the outbreak, but coronavirus does not yet constitute a pandemic.
Meanwhile, the University of York confirmed that a student who contracted coronavirus returned to his apartment but did not come into contact with other residents.
The unnamed student, who is being treated with a relative at a specialist facility in Newcastle, was not in the Vita Student block when he came into contact with the virus but "did return to their room on one occasion and stayed overnight", the university said, as it moved to reassure other students.
In statement on Tuesday, it said: "During this brief period the student did not meet other residents or staff at the building or make use of the communal facilities."
Elsewhere, Public Health England (PHE) confirmed a Belgian woman on board the same French flight that brought back UK citizens from China on Sunday has tested positive for the new strain.
Nick Phin, PHE's National Infection Service deputy director, said: "All of the individuals who were on this flight are currently in supervised isolation and are being monitored for symptoms."