The play revolves around the meeting of Alice Liddell Hargreaves (Dench) and Peter Llewelyn Davies (Whishaw) at the opening of a Lewis Carroll exhibition in 1932, when the original Alice in Wonderland came face to face with the original Peter Pan.
Alexander, who plays Peter Pan, has been seen onstage in Mercury Fur (Old Red Lion Theatre) and The Aliens (Bush Theatre).
Bentall, who plays Alice in Wonderland, has appeared at the National Theatre in Hansel and Gretel, Grief, The Miracle, DNA and Shoot/Get Treasure/Repeat.
Braschi, who plays Arthur Davies/Reggie Hargreaves/Michael Davies, has previously worked with Grandage in Richard II and King Lear (also national tour and Brooklyn Academy of Music).
Farrell, who plays Lewis Carroll, was last seen on the London stage in the transfer of South Downs and The Browing Version for Chichester Festival Theatre to the Harold PInter Theatre.
Riddell, who plays JM Barrie, has worked at the Royal Exchange Theatre in Manchester, the Traverse in Edinburgh, the Tron in Glasgow, and for the RSC and Shared Experience.
To book tickets, contact the box office on 0844 482 5141 or visit www.michaelgrandagecompany.com.