He was due to play a concert in London on Wednesday and the band have said it will go ahead as a tribute to Sudden.
Sudden, who was 49, had recorded under various guises since the 1970s, recording one album with REM members Peter Buck, Bill Berry and Mike Mills.
He also formed the band Swell Maps as a teenager in Solihull in 1972.
During his career he also recorded with Sonic Youth, The Flaming Stars and Voodoo Witch.
Much of his back catalogue has recently been reissued and he was working on his autobiography and a book about Ronnie Wood, citing the Rolling Stones as his favourite band.
His Jacobites bandmate Dave Kusworth said Sudden had been working on new material for an album which fans should eventually get the opportunity to hear.
His record company, Secretly Canadian, said in a statement: "It was a great honour to work with such a legendary figure, and his warmth and generosity of spirit will not be forgotten. He was a good man in endless pursuit of his artistic dreams."
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