British scientist Dr. Robin Shattock told CNBC on Tuesday the public shouldn't expect a coronavirus vaccine to hit the market until early next year, despite recent advances.

"The closest we'll get to making this available will be early next year, or later," Shattock, head of mucosal infection and immunity at the Department of Medicine at Imperial College London, said on "Squawk Box."

"It still requires a lot of testing to see if these vaccines are safe and then see if they work," he added.

Shattock is part of a team in the U.K. exploring potential coronavirus vaccinations. They have started animal testing. The group hopes to move on to human testing "within a period of months," he said.

"We, and the other teams around the world, have moved much faster than has been done before," Shattock said, which he attributed to Chinese health officials sharing their data on the infection.

Health officials around the world are also scrambling develop a vaccine to fight against the rapidly-spreading coronavirus, which was discovered Dec. 31 in the Chinese city of Wuhan in Hubei province. China's National Health Commission said a total of 42,638 coronavirus cases have been confirmed so far, and 1,016 people have died in China from the illness.

A handful of groups and companies, including U.S.-based Johnson & Johnson, have joined the race to find a vaccine for the new virus.

J&J chief scientific officer Paul Stoffels told CNBC late last month that he believes the drugmaker can create a vaccine in the coming months. But like Shattock, Dr. Stoffels also said it would not hit the market for a year.

Additionally, the National Institutes of Health, the National Institute of Allergy and Infectious Diseases, and the Vaccine Research Center is working with Moderna to develop a vaccine, which could start human safety testing in less than three months.

"What is exciting is by having multiple teams working on the same target, we hope more than one candidate will come through, and it will mean there's plenty in terms of scale and supply chain, to act as sufficiently as possible," Shattock said.

A vaccine can't come too soon.

The director-general of the World Health Organization on Tuesday warned that while almost all of the confirmed coronavirus cases are in China, the outbreak constitutes a "very grave threat" for the rest of the world.

Tedros Adhanom Ghebreyesus' comments come less than 24 hours after he told reporters at the U.N. health agency's headquarters in Geneva that cases detected outside China "could be the spark that becomes a bigger fire."

— Reuters contributed to this report.