The actresses will join Tipping The Velvet star Rachel Stirling and Sophie Rundle of Julian Fellowes's Titanic in the four-part ITV series.
The Bletchley Circle centres on a group of codebreakers who leave their quiet post-war lives behind and use their skills to solve a murder.
"The Bletchley Circle combines a vivid portrait of post-war Britain with a taut and original thriller," said Laura Mackie, ITV's head of drama commissioning.
"I'm delighted that we've attracted such a strong cast to bring it to life."
Filming of the programme will begin in London at the end of April.
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