LONDON – There appears to be a special radiance surrounding a star presence – or, if you want to be fancy or fanciful, “aura” – that has little to do with either the confidence of the performer or the expectations of the audience.

But if stellar appeal were to result from nothing more, then anyone with bursting assurance and a well-oiled publicity campaign could shine. As we all know, this is far from so.

There are two actors at present playing in London who have that star presence, even though the quality is much easier to recognize than describe.

At first glance, Peter O’Toole, dazzling audiences in Keith Waterhouse’s “Jeffrey Bernard Is Unwell” at The Old Vic, and Olympia Dukakis, making an acclaimed London debut in Martin Sherman’s one-person play “Rose,” seem to have little in common – apart, perhaps, from being Oscar winners.

What they also share is the rare ability to dissolve that fourth wall between actor and audience, and to appear in character with extraordinary naturalness.

They have that happy, virtually improvisatory air of making up the whole thing as they go along, not so much as if they were living a life, but as if they were telling a story. This is narrative acting par excellence.

“Jeffrey Bernard” is a strange creature of a play, a kind of caricature documentary based on a remarkable character from London’s Soho, Bernard: journalist, drunk, compulsive gambler, layabout and caustic wit.

Bernard was a real-life regular in Soho’s best-known bars. And Waterhouse’s play is set in one of them – the Coach and Horses. After being marooned in the men’s room in an alcoholic miasma, Bernard emerges to find the bar locked up for the night.

With the aid of flashbacks, he regales the audience with a wittily edited account of his life and times.

Although the play was constructed and written by Waterhouse, most of the words are Bernard’s own, culled chiefly from his popular column, “Low Life” – subtitled “a suicide note in weekly installments” – which for years was a regular feature of the English political magazine The Spectator.

Even the title comes from those columns, for on those not-so-infrequent occasions when Bernard was too incapacitated to contribute his piece, his editor would just enter the rubric “Jeffrey Bernard Is Unwell” and all his steady readers would get the message.

O’Toole created Bernard’s stage persona when the play was new 10 years ago, and played it on and off for a couple of seasons. Succeeding him – the play was a considerable West End hit – were Tom Conti and James Bolam; the latter was the Jeffrey Bernard in residence when I first saw the play.

Bolam was so good I could scarcely credit those who told me O’Toole was better, but now I’ve seen O’Toole, and yes, O’Toole is better.

Ever since “Lawrence of Arabia,” O’Toole has been overrated as a movie icon and underrated as an actor, with dire results for his career. O’Toole has pure genius as an actor, not always revealed and certainly not always understood.

Ironically, this Old Vic Theater has bizarre associations for him. In 1964, O’Toole played the title role in a Laurence Olivier staging of “Hamlet,” the very first production of Britain’s then brand-new National Theater.

It was a thrilling, intellectually challenging – and brutally criticized – performance. At the same theater, in 1980, O’Toole was in a legendary production of “Macbeth,” which apparently everyone found laughable.

Now the last Old Vic laugh is with O’Toole, for his present show is the hottest ticket in town.

In a production graced by John Gunter’s realistic design and a supporting cast of four superbly protean actors, he is entrancing everyone, even the London critics, with this delicately funny and gently melancholy study of booze and friendship.

It would be great if Peter O’Toole, “Jeffrey Bernard” and its Soho bar could make it to New York – I suspect it would wrongly be regarded as “too English” – yet I have no doubt that sooner rather than later, “Rose,” I hope with Dukakis, will arrive Stateside. It’s a natural.

Philadelphia-born, London-based playwright Martin Sherman – best known for his 1979 play “Bent” – has devised a long-winded, simplistic monologue about a feisty Jewish woman who has traveled from the Warsaw ghetto and the Holocaust, via the ill-fated voyage of the refugee ship Exodus, to running hotels in Atlantic City and Miami Beach.

No contemporary Jewish cliché is left unclenched and a few are casually explored – such as some American-Jewish generational guilt over Palestine and Israel – but from first to last, the show seems as predictable as a calendar. Yet here the play is not the thing.

The thing, gorgeously, is Dukakis. And now, with the National Theater in this exultant London debut, she finds the role of her life, sustaining it with startling, if underplayed, brilliance.

It seems that a number of Londoners believe she’s Jewish – where do they think the name Dukakis came from? – but believe me, Molly Picon herself could not have done it better.

Dukakis is adorable, touching, dryly amusing, ironic, even at times tragic in these pseudo-reminiscences that are perhaps too good to be true, rather than too true to be good.

But nothing can take away from Dukakis’ triumph. Like O’Toole’s legendary boozer, her Rose is a sweet, sure and simple demonstration of star presence and its star power.