Something is stirring in London’s West End. When did it last boast two theatrical dames in new plays? Helen Mirren plays the Queen again, in Peter Morgan’s first new work since Frost/Nixon. The Audience (Gielgud Theatre, from 15 February) imagines the monarch’s meetings with various PMs, including David Cameron. Another extraordinary meeting – between the real-life Alice (of Wonderland fame) and Peter Pan – reunites Judi Dench with her Bond co-star Ben Whishaw for Peter and Alice (Noël Coward Theatre, 9 March). The latter is part of the Noël Coward Theatre’s Michael Grandage season, which continues with Daniel Radcliffe in Martin McDonagh’s The Cripple of Inishmaan (8 June), David Walliams and Sheridan Smith in a sexed-up Midsummer Night’s Dream (7 September) and Jude Law’s Henry V (23 November).

Heavyweights abound: James McAvoy’s Macbeth (Trafalgar Studios, 9 February), Zoë Wanamaker in Peter Nichols’s Passion Play (Duke of York’s Theatre, 1 May) and Kristin Scott Thomas in OldTimes (Harold Pinter Theatre, 12 January). Fans of musicals have even more to celebrate. Two Broadway hits arrive in London – The Book of Mormon (Prince of Wales Theatre, 25 February) is outrageous, while Once: the Musical (Phoenix, 16 March), adapted from the indie film, bursts with heart. Before the year is out, the National Theatre will stage the delayed Tori Amos musical The Light Princess.

Apart from watching Adrian Lester’s Othello at the National (April), Shakespeare fans should leave London. Jonathan Slinger tackles Hamlet at the Royal Shakespeare Theatre in Stratford-upon-Avon (14 March) and Kenneth Branagh plays Macbeth at the Manchester International Festival in the summer. Tom Morris and Handspring reunite for the first time since War Horse for A Midsummer Night’s Dream at the Bristol Old Vic (28 February).

Back in the capital, Joe Wright makes his theatre directorial debut with Arthur Wing Pinero’s Trelawny of the Wells (Donmar Warehouse, 15 February). Let’s end on new writing for the New Year. Look out for work by Arinze Kene (God’s Property, Soho Theatre, 26 February) and Lucy Kirkwood (Chimerica, Almeida, 17 May).