Chris Hill, 38, lives there with his wife, Caitlyn Gao, and daughter, Renee Gao, who are both Chinese citizens.
Mr Hill, who is from Sunderland, said British officials leaving the country was "not a good sight".
The government has said it would have "limited" ability to help Britons after withdrawing all but essential staff.
Mr Hill said: "My only worry now is after everybody pulls out the FCO [Foreign and Commonwealth Office] will forget about those who are staying and not give any support for us.
"For British nationals that are staying in Wuhan, but also in China, to have the consulate and embassy evacuating, it's not a good sight to see really, is it?
"My concerns would basically be that they're going to completely write off China in the long run.
"Even though they say that they are trying, it's also a fear that with pulling all the staff out, they're just going to go 'out of sight, out of mind' kind of thing."
Mr Hill was told he, his wife and four-year-old daughter would be able to board an evacuation plane bound for France.
However, he says his wife is unable to leave because she is a nurse at a hospital and is also unwilling to leave her parents.
"I am not willing to leave her behind and take my daughter," Mr Hill said. "It's either we all go, or we all stay in Wuhan."
Dozens of UK nationals arrived home on Friday after being flown out of China. They will spend two weeks in quarantine at Arrowe Park Hospital in the Wirral.
The Foreign Office has been approached for comment.
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