Cooney himself will also appear in the production which, as previously announced, runs from 19 March to 26 April 2014 (previews from 8 March).
The 1984 play centres on a wayward MP (Praed) who is struggling to conform to prudish Prime Minister Margaret Thatcher's puritanical approach.
Others in the cast of the Menier revival include Jean Fergusson, Jeffrey Holland, Nick Wilton, Kathryn Rooney, Kelly Adams and Tom Golding.
Michael Praed rose to fame in TV series Robin of Sherwood and Dynasty, while theatre credits include Aspects of Love (West End), The Sound of Music and High Society (UK Tours). Josefina Gabrielle returns to the Chocolate Factory after playing Gussie Carnegie in Maria Friedman's award-winning revival of Sondheim's Merrily We Roll Along.
Casting has been announced for New Adventures and Re:Bourne's forthcoming national tour of "a thrilling new large-scale dance spectacular" production of Lord of the Flies, choreographed by Scott Ambler and adapted and directed by Ambler and Matthew Bourne.
The production opens at The Lowry, Salford, from 2 to 5 April 2014, before touring to venues nationwide. It will run at Sadler's Wells from 8 to 11 October.
The company includes New Adventures dancers Sam Archer as Maurice, Luke Murphy as Sam, Dominic North as Ralph, Sam Plant as Piggy, Alastair Postlethwaite as Eric, Danny Reubens as Jack and Dan Wright as Roger.
Making their New Adventures debuts in the production will be Layton Williams as Simon and Jack Hazelton. The young people cast in the production will be unique to each region and will be announced for individual venues shortly.
Bourne said: "Lord of the Flies is a project never before mounted on the large-scale... I look forward to an exciting, and for some, life-changing year ahead".