Fox (A Midsummer Night's Dream, Southwark Playhouse) and Morgan (Red Velvet, Garrick) will also be joined by Clare Foster (Merrily We Roll Along, Menier and West End), Forbes Masson (Doctor Faustus, Duke of York's), Peter McDonald (The Weir, Donmar) and Sarah Quist (The Amen Corner, National Theatre).
Patrick Marber directs the new production – the first London revival in over 20 years – with design by Tim Hatley.
Stoppard's comedy premiered at the Aldwych Theatre in 1974 and won the Evening Standard Award for Best Comedy along with a Tony Award for Best Play for its Broadway transfer
The play centres on British diplomat Henry Carr and his encounters with the likes of James Joyce and Lenin during the First World War
Travesties runs at the Menier Chocolate Factory from 4 October – 19 November 2016, with previews from 22 September.