In a statement, her family said she died peacefully of natural causes at home in Lewes, East Sussex.
Blackman was also known for playing Cathy Gale in the 1960s TV series The Avengers opposite Patrick Macnee.
The pair had a novelty hit with 1964's Kinky Boots, which reached the Top 10 in 1990.
Her other roles included Hera in Jason and the Argonauts and Laura West in 1990s TV series The Upper Hand.
The statement issued by Blackman's family said: "As well as being a much adored mother and grandmother, Honor was an actor of hugely prolific creative talent.
