Old Trafford, home of Manchester United, is renowned as the Theatre of Dreams. I've never been there, although I wrote once to the manager and secretary of the club offering my services as a ten-year old footballer.

I got a polite letter back, too, of the "thank you, we'll let you know..." variety, but at least I had acquired a treasured piece of headed notepaper. And these days I can visit other theatres of dreams without taking my soccer boots, even if, in the charmless words of Charles Spencer's recurring phrase, I am moved to administer "a good kicking."

This week so far I've visited two such dream venues: the Old Rep in Birmingham and the new Olympic Park in Stratford East, the nearest we've come, in that Cockney part of the world, on my home patch, to Joan Littlewood's long-ago plans for a Fun Palace.

The Old Rep, hard by New Street Station, is one of the venues currently used by the Birmingham Rep while the unlovely 1971 concrete building is re-developed as part of the Library of Birmingham, reopening next year under the artistic directorship of Roxana Silbert.

The Old Rep was founded in 1913 by the independently wealthy Sir Barry Jackson and housed the first major work of Peter Brook, Laurence Olivier, Edith Evans, Paul Scofield, Albert Finney and Derek Jacobi, to name but several. It's a perfect small stage and auditorium, with a magic all of its own, not of ghosts, exactly, but of great deeds, certainly; I sensed this even when I last went there some years ago for a touring children's play by David Wood.

And returning this week for Calixto Bieito's transfixing Shakespearean mash-up, Forests, co-produced by the Rep with the RSC as part of the World Shakespeare Festival, I found myself wondering, all over again, why on earth would the Rep have wanted to leave this place at all?

Forests is in itself something of a dream play, a fluently arranged series of Shakespearean scenes revealing the human soul and predicament in the landscape of Arden, Birnam Wood and the blasted heath that is entrancing, alienating, dangerous and cruel.

We move, in fact, from the Garden of Eden to the battlefields of the Wars of the Roses and the remote cave of Timon. The seven actors are first seen in an art gallery, where a large tree is raised on a plinth. Half way through the show, that plinth will disintegrate in an earthen landslide, enveloping them in an avalanche of  sexual confusion, violence and murder.

Bieito is remembered here as the Barcelona bad boy, the one whose production of Verdi's A Masked Ball at ENO opened with fourteen men sitting in transparent cubicles with their trousers round their ankles.

Cries of cultural vandalism are quite often the refuge of puritans and scoundrels unprepared to make the sort of imaginative leaps of faith directors like Bieito - and there aren't too many of them - demand we credit to the greatest of theatrical artists.

It's as though, with Forests, he's grown tired of conventional narrative, even in Shakespeare, and tried to wrestle the essential meaning and provocation of the greatest plays, and some of the lesser ones, too, to the ground.

And there are so many speeches you hear again as if for the first time, plucked from the wilder reaches of Henry VI, or Titus Andronicus, or Timon of Athens, as well as from the sonnets and Venus and Adonis

It's amazing how beautiful Shakespeare sounds in Catalan, too. I'm told there's a great tradition of Shakespearean translation in that language and I'm not at all sure that I don't prefer the great despondency speeches of Richard II and Henry VI in their new cloak.

The show, mostly in English, is sur-titled throughout, beautifully lit by our own Tim Mitchell, with fantastic songs by gypsy rock troubadour Maika Makovski. Four of the cast are British, and all from totally different traditions: Hayley Carmichael from "physical theatre" and Told By An Idiot; George Costigan from the 1970s Liverpool Everyman; Christopher Simpson from the Bush, Cardboard Citizens and Spooks on telly; and Katy Stephens from Michael Boyd's RSC, where she has played Rosalind and Goneril.

I came straight from Birmingham to attend Ruth Mackenzie's last London 2012 festival press conference in King's College in the Strand, where Bieito explained himself, gently and persuasively, to an admittedly fairly docile audience.

He quoted Bertrand Russell, Beckett and Schopenhaur on the twin characteristics of jungle and tundra in Shakespeare's forests, acknowledging the influence in all his work of Bunuel and the propensity of all humans to fall in love not just with each other, but with trees, too.

After so much talk, it was time for action down Stratford way, and the Olympic Park is every bit as terrific as everyone says. I got a bit fed up with the announcer using the word "inspirational" every five seconds, but then the Paralympians themselves justified his tedious vocabulary at every hop, skip and jump of the way.

There was one unintentionally hilarious moment when a guide runner got tangled up with his blind charge and the two of them were left sprawling on the track 30 yards from home. But even that mini-disaster had a heart-warming conclusion.

Another highlight, following the chorus of disapproval that met Chancellor George Osborne when he appeared to present medals on the previous evening, was the concerted booing of Home Secretary Theresa May when she took on the same duty last night.

Just to rub it in, the announcement of the Duke of Wessex, Prince Edward, patron of the National Youth Music Theatre, was met with a sustained, resounding cheer. Down with politicos, up the royals! 

But nothing matched the noise we raised for David Weir, the astonishing wheelchair athlete who stormed home, as if borne on a tide of sound, to win his second gold of the Paralympics in the 1500 metres.

There were 80,000 of us packed into the stadium. And yet, thanks to the brilliance of the volunteer ushering, we were home on public transport well within the hour. I wonder if things will run as smoothly once West Ham United are confirmed (as surely they must be) as the long-term tenants of the stadium with crowds only half that size.

The football team is unhappy about the insistence of the authorities that the running track remains around the pitch. I see no problem. The whole place is vastly superior to, and far more intimate than, the new Emirates stadium for Arsenal; almost as cosy, in fact, as the Old Rep in Birmingham.