The musician passed away after a long period of ill health, his manager Pamela Sutton said.
"(Acker had) been ill for some time. He was my great friend and his music was legendary," Sutton said.
The Somerset-born musician emerged as a major figure in the traditional jazz revival in the 1950s and 1960s.
He was best known for his song 'Stranger on the Shore', which was the UK's biggest selling single of 1962. The Ivor Novello award winner also had hits with 'Summer Set' and 'Buona Sera'.
Bilk is survived by his wife Jean and two children.
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