How often are you charmed by one of Shakespeare’s sylvan romances while literally under a greenwood tree? Even if this summer is proving rather generous with the rough weather, it is an unusual pleasure to wander around a fine woodland garden while Rosalind and Orlando pursue their light-hearted crossdressing courtship in the forest of Arden, and white sheets inked with bad love poems flutter from the trunks of many oak trees.

It begins promisingly, a dark Gothic fairy tale – both Grimm and grim. The writhing witches (four, oddly) are summoned from a pile of dead bodies, Stefan Fichert’s eerie puppetry all chopped-up limbs and interchanging demonic heads, hands scuttling across the floor like a spider, and disembodied voices chanting and haunting. Then the spell is broken and “what seem’d corporal melted”.

As we finally go to the polls, casting votes based on our view of national identity and Britain’s place in the world, here comes Shakespeare’s ever-topical play. Robert Hastie’s thoughtful take is contemporary dress but stripped back, not so much holding up a mirror as inviting us to project modern concerns onto it.

There's a one-man play inside every politician – and a one-woman play behind each male leader. Linda Griffiths's and Paul Thompson's solo show, Maggie and Pierre, explores Maggie Trudeau's struggle with bipolar disorder and her temptestuous relationship with Canadian Prime Minister Pierre Trudeau (father of current PM Justin Trudeau). Written in 1979 but only now receiving its European premiere, this is an ambitious attempt to explore the personal fissures that politics creates.

In the town of Nizhny Novgorod where Maxim Gorky was born, it was said that “the houses are made of stone, the people of iron”. Vassa Zheleznova, the titular matriarch of this rarely performed play, is one such person. She is a businesswoman of steely will and juggernaut energy whose tragedy is to see her family destroyed by the same bourgeois values that she has fought so fiercely to preserve.

Who do you trust? The EU Referendum campaign has exposed a mounting suspicion of the establishment, from financial institutions to press and politicians, and our sense of nationhood has never been murkier. But if we cease to believe in anything, how does that affect our sense of self?

Harold Brighouse's time-honoured English comedy from a century ago survives, its virtues mostly intact especially once attention shifts away from the snarling patriarch of the title, Henry Horatio Hobson (a padded Martin Shaw), to the generation of women beneath him – his peppery, politically and socially progressive eldest daughter, Maggie (Naomi Frederick), chief among them.

"I can add colours to the chameleon," Richard III remarks of himself early in his anguished, marauding ascent to the throne, and the description could equally apply to the electrifying actor, Ralph Fiennes, who is London's latest hedgehog/dog/toad/bottled spider (pick your animal imagery of choice).

Polymath playwright Philip Ridley is endlessly inventive. Having written a couple of exciting pieces of bravura storytelling – Tender Napalm (2012) and Dark Vanilla Jungle (2014) – he went on to pen a political comedy – Radiant Vermin (recently revived at the Soho Theatre) – about the housing shortage, with three actors directly addressing the audience, and now he’s back with yet another kind of play: this time it’s a truly epic fantasy in a found space.

If anyone harboured any doubts as to how diverse the world of musical theatre can be, this past week will surely have proved an ear and eye-opener. While Richard  Taylor and David Wood's poetic take on The Go-Between pretty much threw out the rule book on musicals, Disney's stage version of their blockbuster film Aladdin dutifully returns to the first edition, which is how a successful franchise works. As the old adage goes, "if I knew the secret I'd bottle it". Disney has – and pantomime has come early to the West End.