Roger Hallam, 58, was jailed for five years after being found guilty of conspiracy to cause a public nuisance for his involvement in the protest.
Cressida Gethin, 22, Daniel Shaw, 38, Lucia Whittaker de Abreu, 35, and Louise Lancaster, 58, were jailed for four years over the demonstration, which saw 45 people climb on to gantries over the motorway.
The letter said: "With prisons at breaking point and the new government acting urgently to address this, how can these sentences be seen as anything other than insanity?
Describing the sentences as "one of the greatest injustices in a British court in modern history," the letter states: "The sentences, ranging from four to five years, are higher than those given to many who commit serious sexual assault."
The jail terms are thought to be the longest sentences ever given in a UK court for a peaceful protest.
Prime Minister Sir Keir Starmer has faced calls to intervene in the case while UN human rights commissioner Volker Turk described the sentences as "deeply troubling".
Among the signatories are top human rights lawyer Sir Geoffrey Bindman KC, artist Dame Tracey Emin, Coldplay frontman Chris Martin, film director Danny Boyle, author Sir Philip Pullman, singer Annie Lennox, actor Toby Jones, Jeremy Corbyn MPand John McDonnell MP.
The signatories argued that the non-violent protesters were "fulfilling a necessary service by alerting the nation to the grave risk we all face, as scientists in their droves express their fear that many of the Earth's systems are already at breaking point".
A spokesperson for the Attorney General's Office said: "Decisions to prosecute, convict and sentence are, rightly, made independently of Government by the Crown Prosecution Service, juries and judges respectively. The Attorney General has no power to intervene in these cases."