Sir Derek Jacobi and Mark Rylance (left and right) are in the group
Almost 300 people have signed a "declaration of reasonable doubt", which they hope will prompt further research into the issue.
"I subscribe to the group theory. I don't think anybody could do it on their own," Sir Derek said.
The group says there are no records of Shakespeare being paid for his work.
While documents do exist for Shakespeare, who was born in Stratford-upon-Avon in 1564, all are non-literary.
In particular, his will, in which he left his wife "my second best bed with the furniture" contains none of his famous turns of phrase and it does not mention any books, plays or poems.
Illiterate household
The 287-strong Shakespeare Authorship Coalition says it is not possible that the bard's plays - with their emphasis on law - could have been penned by a 16th Century commoner raised in an illiterate household.
The group asks if one man alone could have come up with his works
"How did he become so familiar with all things Italian so that even obscure details in these plays are accurate?" the group adds.
Conspiracy theories have circulated since the 18th Century about a number of figures who could have used Shakespeare as a pen-name, including playwright Christopher Marlowe, nobleman Edward de Vere and Francis Bacon.
"I think the leading light was probably de Vere as I agree that an author writes about his own experience, his own life and personalities," Sir Derek said.
The declaration, unveiled at the Minerva Theatre in Chichester, West Sussex, also names 20 prominent doubters of the past, including Mark Twain, Orson Welles, Sir John Gielgud and Charlie Chaplin.
'Legitimate question'
A copy was presented to Dr William Leahy, head of English at London's Brunel University and convenor of the first MA in Shakespeare authorship studies, to be launched later this month.
"It has been a battle of mine for the last couple of years to get this into academia," Dr Leahy said.
"It's a legitimate question, it has a mystery at its centre and intellectual discussion will bring us closer to that centre.
"That's not to say we will answer anything, that's not the point. It is, of course, to question."
William Shakespeare, 16th century playwright. 
A debate has been launched by almost 300 people, seeking further research into William Shakespeare and the many masterpieces attributed to him. The group, named the Shakespeare Authorship Coalition, are reluctant to believe that the Bard wrote all of the plays that make him internationally famous, and are keen to unravel the mysteries surrounding his life and work.

Although it is widely accepted that Shakespeare existed and penned many works, the group question why all records of Shakespeare are non-literary, and how so many high-quality plays could be written by someone born into an illiterate household. The Coalition also asks why none of his plays mention his home town of Stratford-upon-Avon, and also how a 16th Century commoner could have such extensive and accurate knowledge of the worldwide settings in which they take place.

Conspiracy theories since the 18th century have claimed that the works could have been written by authors using the pen name Shakespeare, particularly Francis Bacon, Christopher Marlowe and Edward de Vere. Sir Derek Jacobi, actor and member of the Shakespeare Authorship Coalition, believes that the famous plays could have been written by more than one writer. "I subscribe to the group theory," Sir Derek said. "I don't think anybody could do it on their own." 

A "declaration of reasonable doubt" was presented to Dr William Leahy, Head of English at London's Brunel University. Speaking about the conspiracies, he said, "It's a legitimate question, it has a mystery at its centre and intellectual discussion will bring us closer to that centre." 

The Coalition has set up a website, inviting people to sign the declaration and keep up-to-date with new research.