The open letter in the Daily Mail newspaper, which comes after the release of a US Senate report into the torture of Al-Qaeda detainees, said that Shaker Aamer's continued detention was "shocking".
The 46-year-old's wife and four children live in London.
Pink Floyd co-founder Roger Waters, singer Sophie Ellis-Bextor and comedian Frankie Boyle were among the signatories, joined by some MPs from the ruling Conservative and opposition Labour parties.
"Habeas corpus" is a form of legal redress against unlawful imprisonment and was a key point in the Magna Carta charter drawn up by King John of England in 1215 and often seen as the world's first constitution.
Also Read
"The British government has a non-negotiable responsibility to secure the return of Mr Aamer, given his status as a legal British resident," the letter said.
The letter said that Aamer had twice been cleared for release by US authorities in 2007 and 2009 but that this had never gone ahead and that there may be plans to deport him to his native Saudi Arabia.
Aamer is alleged to have been a key Britain-based recruiter and financier for the Al-Qaeda militant network and allegedly worked for Osama Bin Laden in Afghanistan, according to US military documents.
He was captured in Tora Bora in northern Afghanistan in December 2001, transferred to Guantanamo in February 2002 and has been held there ever since.
He is considered "high risk" and "likely to pose a threat to the US, its interests and allies", the US military says.
Four Syrians, a Palestinian and a Tunisian left Guantanamo earlier this month for Uruguay, bringing the number freed so far this year to 19.