Every year there’s an adorable new starlet at the Oscars. Still new to the scene, they don’t know they’re supposed to play it cool at these awards shindigs, and their innocent excitement proves infectious to the public. Last year it was Timothée Chalamet, 22 when he was nominated for best supporting actor in his first major role. Previously it was Quvenzhané Wallis, nine years old when she was nominated for Beasts of the Southern Wild. This year’s adorable whippersnapper is 61-year-old Richard E Grant, veteran of a mere 100-plus movies.

“This experience has been beyond anything I could imagine. You always think you won’t get awarded for things. That’s only for the elites: the Denches, the McKellens, and so on,” says Grant down the phone from Los Angeles.

Does he think he’ll be able to play it cool on the night? “I very much doubt it! Ha ha! I’ll never forget this ride for the rest of my life.”

The day it was announced that Grant could add a best supporting actor Oscar nomination to his already heavily garlanded pitch-perfect performance as the rakish rogue Jack in Can You Ever Forgive Me?, he posted a video on Twitter.

It showed him standing outside a house in Notting Hill which, he explained, he’d lived in 36 years ago when it was a bedsit. “I cannot believe I’m standing here, as an almost 62-year-old man, having an Oscar nomination! Haaa!” he cheered, his voice cracking.

Grant has since chronicled his exciting journey through awards season with gusto. Last month he tweeted a photo of himself outside Barbra Streisand’s home, alongside a letter he’d sent to her when he was 14. Streisand tweeted back congratulations for his nomination adding, as if he were 21 rather than 61: “Look at u now!”

“I crumpled up when that happened. That seed of approval from her was the highest affirmation you could wish for as a fan, even if it came 47 years after I wrote the letter,” he says. He adds, a little superfluously: “I never matured into the age when you’re able to hide your adulatory feelings as a fan.”

He also excitedly tweeted selfies of himself with Bradley Cooper, Lady Gaga and other nominees at the traditional Oscars luncheon. The day before we speak, he described himself as “a temporary A-lister”. And the media have been eating it up, with headlines such as: “Richard E Grant’s Unbridled Joy Is the Best Thing About Awards Season.”

It has all been rather charming to watch, no question, if somewhat bewildering for longtime Grant fans. Er, Richard, haven’t you been on the A-list for a while?

“No no, not at all! I understand that how you perceive yourself and how others perceive you don’t always match, but no, no, no,” he insists.

But in your memoir, With Nails, you describe being directed by Robert Altman, Francis Ford Coppola and Martin Scorsese. Are you really overcome with excitement about meeting, say, Lady Gaga?

“Oh God, yeah,” he says. “It genuinely feels like Madame Tussauds surreal. People I’ve always admired and newly admired all in one place – I really don’t know how other people are so cool about it.”

Whether Grant really is as thrilled by the razzle-dazzle as he seems on social media, or if he and his producers are playing a clever game in their Oscars campaign to out-manoeuvre the current frontrunner in his category, Mahershala Ali for Green Book, his nomination is both deserved and overdue. Even aside from his signature performance in Withnail & I (which we’ll return to), Grant has been one of the most dependable character actors around for decades, and his supporting performances often show him at his best.

In Steve Martin’s magical 1991 film LA Story, Grant took what should have been a thankless role, the twittish English ex-husband of Martin’s prospective girlfriend (Victoria Tennant), and turned him into a hilariously camp creation, so fully rounded you wished there could be a sequel just about him. The following year, in Altman’s The Player, he was in many ways the heart of the movie, the idealistic writer who sells out to Hollywood, and more than held his own alongside the film’s star, Tim Robbins, and the slew of A-list cameos. More recently, he has made pleasing appearances in some of the most popular TV shows, including Game of Thrones, and Downton Abbey.

It has always seemed as if Grant emerged from an earlier, more proper age, an impression mined by, among others, Scorsese who cast him in The Age of Innocence, as well as by Downton Abbey. His almost caricature Englishness may stem from his upbringing in Swaziland during the last days of empire, which he chronicled in his 2005 film, Wah-Wah. He made what remains one of the greatest film debuts of all time, when he was cast as Withnail in his first film role, but the movie was infamously something of a bust when it was released.

Grant then hacked his way through the British film industry, including a splashy starring performance in How to Get Ahead in Advertising (in which he uttered the timeless line: “I’m an expert in tits, tits and peanut butter!”). He then crossed over to Hollywood to appear in supporting roles in movies such as the unjustly forgotten Henry & June and the justly derided Hudson Hawk. He briefly tried to capitalise on the mid-90s vogue for romcoms featuring British men with charming accents in Jack & Sarah (1995), but he is always at his best playing characters with more spice than sugar. Which is why, 30-odd years on, he has still not escaped from Withnail’s shadow and never will.

As many reviewers have pointed out, his character in Can You Ever Forgive Me? feels a lot like the evolution of Withnail – after all, dealing drugs and conning middle-aged ladies in New York seems a fairly plausible career for a sixtysomething Withnail. Is there a part of Grant that hopes that all the attention he’s received for this performance will bloody well stop people from asking him about Withnail every day of his life?

“Oh no, not at all, because that implies it’s a burden, and it really isn’t. I’m honestly so grateful to be attached to a movie that has an ongoing cult status,” he says.

So, given how much energy he’s put into celebrating his nomination, has he thought about how he’ll celebrate if he wins? Surely the finest wines available to humanity are in order. (Alas, despite being so good at playing drunks, Grant is teetotal.)

“Gosh, no,” he says, sounding genuinely flummoxed. “I really haven’t considered that because it’s so clear who the frontrunner is. I’m just enjoying the spectacle.”

• Can You Ever Forgive Me? is on release; the Baftas are on Sunday 10 February