A Streetcar Named Desire, NT Lyttelton, London Elaine Stritch at Liberty, Old Vic, London King Lear, Swan, Stratford-upon-Avon

The temperature is rising in A Streetcar Named Desire. That's clear as soon as Blanche DuBois materialises at the dilapidated New Orleans tenement where her younger sister, Stella, lives with brawny Stanley Kowalski. Blanche is dressed up to the nines while Stanley, stripping off his shirt, is a far cry from the refined gents of the siblings' well-to-do early years.

The temperature is rising in A Streetcar Named Desire. That's clear as soon as Blanche DuBois materialises at the dilapidated New Orleans tenement where her younger sister, Stella, lives with brawny Stanley Kowalski. Blanche is dressed up to the nines while Stanley, stripping off his shirt, is a far cry from the refined gents of the siblings' well-to-do early years.

Trevor Nunn's staging of Tennessee Williams' tragedy is also a very hot ticket with Glenn Close starring as the unstable and alcoholic ageing belle who gets under her brother-in-law's skin during one long summer. Indeed, this production can't get enough of vintage ceiling fans. Dozens glint and whirr in the darkness which surrounds Bunny Christie's three-storey set.

That said, I've seen more sexually electric performances of Streetcar. Making her London stage debut, Close certainly proves herself a high calibre actress. Nunn excels at fostering naturalistic acting and Close's Blanche is no exaggerated vamp but a remarkably sympathetic, girlishly playful woman. Close also makes Blanche's uppity airs and graces very funny. Her outrage is priceless when faced with chores – like actually having to dial a lover's number.

On the other hand, Blanche's destructive impulses are played down too much. Close's erotic brushes with Iain Glen's Stanley look peculiarly sudden, this duo's class warfare being more apparent than any simmering sexual tension. Blanche's increasingly histrionic speeches and mad fantasies jolt as well, with Close developing an awkward habit of stepping downstage into a spotlight.

Streetcar's hallucinatory elements need more subtle handling, too, and might have been more smoothly introduced by Williams's vision of a set with translucent walls. In the main, Christie's revolving edifice is a showy imitation of cinematic tracking shots. The mood-enhancing use of jazz and blues is clumsily amplified, as well. So much so you think the show's turning into a musical.

Nonetheless, Nunn's core players still remind you how raw and politically provocative this play must have been in 1947, with its exposure of sexual underworlds and the rough treatment of women and the mentally ill. This Streetcar is far more than a star vehicle too, since the key "supporting" performances are on a par with Close. Though Marlon Brando's iconic Stanley loiters in your mind, Glen's achievement is to be swaggering and sharp-witted. And let's hope we see more of Essie Davis whose Stella – besides looking like the alter ego or steadier woman Blanche might have been – richly blends devotion with slow-burning irritation.

Moving on to another blonde American luminary, Elaine Stritch could probably have drunk Close's Blanche under the table before she dried out a few years back. Elaine Stritch At Liberty is a Tony-winning, solo cabaret show, written in collaboration with author and journalist John Lahr. The droll, now septuagenarian Broadway legend recalls the highs (Sondheim's Company, for one) and bleary lows of her career and private life. En route she belts out favourite numbers, like "I'm still here" from Sondheim's Follies.

Obviously, as they say, the show must go on. And it does, for nearly three hours. I could have done without half the songs and the listing of whole casts from (for most of us) obscure US productions. Nonetheless, some anecdotes are intriguing – not least recalling two drama-school dates with a dreadfully moody, pre-Streetcar Brando. Fundamentally, you can't help liking this splendidly game old bird who wryly strolls on in a shirt and black nylons – no spring chicken but a sassy, elegantly stringy one.

Luring big names has often been a struggle for the RSC. What's striking is the current attempt to make an invigorating drama out of that "crisis" by transfusing new blood into the corps. You're unlikely to recognise a single face in King Lear because the Academy Company – being nurtured in-house by director Declan Donnellan – is composed of drama school graduates.

With many acting courses aiming at screen careers, such supplementary classical training might prove vital for the RSC's own survival. Kicking off with Shakespeare's towering tragedy about old age is also brave, to say the least, when your cast are nearer the playground than the grave. And to Donnellan's credit, numerous flashes of interpretative brilliance illuminate this production – equivalent to the lightning that flares over Nonso Anozie's hulking Lear on the heath.

Performed mainly on a bare stage (designed by Nick Ormerod) in increasingly muddied black tie, scenes are dynamically overlapped, pointedly showing us the outcast Lear and Gloucester in tandem with their morally lost heirs back home. The idea that the King is a dangerous dictatorial showman and unwise joker is also boldly established as Anozie turns the division of his kingdom into a cabaret-cum-game show, summoning his nervously smiling daughters to come on down from the royal balcony.

However, one can hardly claim this debut production has brought to light the next Robert Stephens or Judi Dench. Katherine Manners stands out as a guilt-harrowed Regan, pushed to distraught cruelty by her father's bullying, but Anozie (actually not unlike Close) never goes truly, heartrendingly mad with grief. Still, you can't ask for the world after just 10 weeks of rehearsals. Given more time, the Academy may bear more fruit – assuming Michael Boyd doesn't nip it in the bud when he takes over from Adrian Noble next Spring.

k.bassett@independent.co.uk

'A Streetcar Name Desire': NT Lyttelton, London SE1 (020 7452 3000), to 23 Nov; 'Elaine Stritch At Liberty': Old Vic, London SE1 (020 7369 1722), to 16 Nov; 'King Lear': Young Vic, London SE1 (020 7928 6363), from 23 Oct to 9 Nov