Other statues in the sights of campaigners, who say Britain "must face the truth about its colonial past", include the Oxford tribute to Cecil Rhodes and numerous statues of Robert Peel.
"James Cook invaded Australia just over 250 years ago. He claimed possession over the entire nation even though it clearly belonged to the people already there," the coalition's website reads. "What followed was 250 of genocidal activities and policies based on race that murdered thousands of women, men and children. Captain Cook symbolises racial oppression and violence… [The statues] must be removed."
In June last year a Captain Cook statue in New Zealand was defaced.
Graffiti was sprayed across the monument in Gisborne, which sits alongside the Tūranganui River in Waikanae Park.
The graffiti said "Black Lives Matter and so do Maori" and "Take this racist headstone of my people down before I do". Swastikas were also sprayed on the statue.
It was also defaced in July 2019.
Robert Goodwill, the Conservative MP for Whitby and Scarborough, home to one of the statues and the Memorial Museum, said targeting the memorials was "completely ridiculous".
Robert Goodwill, the Conservative MP for Whitby and Scarborough, home to one of the statues and the Memorial Museum, said targeting the memorials was "completely ridiculous".
"Captain Cook is one of the proudest sons of Whitby. The statue is one of our best known landmarks, and the Captain Cook Museum is one of our most popular tourist attractions," he told The Telegraph.
"They're trying to erase important aspects of our history, and we all need to study history and learn from any mistakes. There were things done in the name of the Empire that would not be acceptable now, but we don't need to expunge them from history."
Tourists visit the seaside town to see the harbour from which Captain Cook first set sail on his voyage, Goodwill said, adding: "We're proud of Captain Cook in Whitby, and we wouldn't countenance any attempts to remove him from the history books."
The statue was designed by sculptor John Tweed and has overlooked Whitby, where all four of Cook's ships were built, since 1912.
Pub chain JD Wetherspoon is understood not to have any plans to rename The Resolution, its Middlesbrough pub named after Cook's flagship, as the chain believes the link is entirely historical.
A spokesman said: "It goes without saying that slavery is abhorrent. We will examine any examples of historical connections which are brought to our attention, including The Resolution, and discuss with customers and staff."
Polling commissioned by the BBC in 2002 saw Cook, who made the first recorded navigations of New Zealand and indigenous Australia, rank at number 12 in the broadcaster's list of the 100 Greatest Britons.
Under new laws outlined by Robert Jenrick, the Communities Secretary, which will take effect in the spring, statues, plaques and memorials will not be removed without a formal planning process, with prominent context being given for more controversial monuments.
In Australia, a bronze statue of Captain Cook in New South Wales which dates back to 1879 was defaced during Black Lives Matter protests in June.
A Ministry of Housing, Communities and Local Government spokesman said: "Any removal should require planning permission and local people given the chance to be properly consulted. That's why we are changing the law to protect historic monuments to ensure we don't repeat the errors of previous generations."
Under threat: Campaign group's targets
Captain Cook statue, Whitby
This has overlooked Whitby harbour since 1912.
Captain Cook statue, London
Completed in 1914, it stands on The Mall, by Admiralty Arch.
Captain Cook Memorial Museum, Whitby
On the harbour side of Grape Lane, it opened in 1986 and holds a VisitEngland Gold Award for Excellence.
Captain Cook Square, Middlesbrough
A retail area that is home to cafes, shops and restaurants.
Captain Cook Crescent, Middlesbrough
A residential street.
James Cook University Hospital, Middlesbrough
A major trauma centre that provides specialist care and treatment.
The Resolution, Middlesbrough
Part of the Wetherspoon chain, it is named after one of Cook's ships.
