From the list of film critics’ first world problems, “party exhaustion” must be among the most supremely dickish, so let me just say that the London Film Festival came to a close with a very full final weekend — in addition to her bold programming and tight organization, Clare Stewart (now in her second year as director of the LFF) has made an already enjoyable festival more convivial and night-owl-oriented than ever before. And indeed, they had much to celebrate this year — not least the world premiere of “Saving Mr. Banks,” a grand coup for a fest that usually cedes such major debuts to the likes of Toronto and New York. Last night’s closing bash, decked out in “Mary Poppins”-themed umbrellas and cherry trees, was suitably boastful.

On Saturday night, however, came a more intimate but equally luxurious event: the festival’s official awards dinner. Taking place once more in Whitehall’s gorgeous 17th-century Banqueting House — a stone’s throw from 10 Downing Street — it was an evening that crowned four deserving winners in the competition categories, though the show was stolen by an honorary British Film Institute Fellowship presentation for 91-year-old legend Christopher Lee.

It was privilege enough to be in the presence of the merlot-voiced star of “The Wicker Man,” the “Lord of the Rings” trilogy and any number of multiple Hammer Horror treasures, but the festival’s choice of presenter made the moment that much more special. We’d been told to expect a surprise, and when a sprightly Joanna Lumley sauntered onto stage to play emcee for the evening, I thought that was rather a nice one: Lumley, as she reminded the audience with relish, shared the screen with Lee 40 years ago in “The Satanic Rites of Dracula.”

But the LFF organizers had something else up their collective sleeve: the hitherto sedate crowd of black-tie-wearing industry folk roared with excitement when Johnny Depp came on stage to hand Lee his award — the BFI’s highest honor, and one he now shares with a host of luminaries from Olivier to Scorsese.

It was a brief presentation, but a highly emotional one. The sincere friendship and mutual respect between these two very different actors — united on four Tim Burton films, most recently “Alice in Wonderland” — was all too evident, as both spoke in tremulous voices and sniffed back a tear or two.

A blond-haired Depp, his Doc Martens shining below his tux, spoke of how Lee’s work has “fascinated and inspired” him from childhood, concluding by calling him “a national treasure and genuine artist.” “I love you,” he finished. Lee, looking frail but visibly moved, countered by saying Depp means “an enormous amount” to him. “He’s one of the few young actors today who’s genuinely a star,” he said. It was sweet to hear the 50-year-old Depp described as a “young actor” — from Lee’s perspective, one can see how it hardly makes a difference.

Lee got several laughs from the crowd in his short speech. “When I take a look back, over 67 years, at the characters I’ve played, I get a truly strange feeling they were all played by somebody else, and not by me,” he said. “There are a few occasions when it has been the case I wish it had! ” It was a sly reference to the fact that much of his most memorable, enduring work has been in the kind of gleefully lurid B-movies that would never have played the London Film Festival back in the day, much less received awards for their actors — which makes this choice of BFI recipient all the more welcome.

It fell to another recent BFI Fellowship honoree — recently retired Observer film critic Philip French, this year’s Competition jury president — to present the night’s top award. The 13-film shortlist for Best Film was full of strong, sometimes unexpected choices: I’d have been happy with a win for Jonathan Glazer’s “Under the Skin,” Xavier Dolan’s “Tom at the Farm,” Clio Barnard’s “The Selfish Giant” or several others.

But I couldn’t argue with the selection of the jury, which also included Miranda Richardson, Lone Scherfig and Oscar-nominated cinematographer Rodrigo Prieto: Polish-British director Pawel Pawlikowski’s lovely new film “Ida” was a comparatively under-the-radar nominee, but one that built deserved word-of-mouth acclaim over the course of the festival. Shot in exquisitely stark black and white, it’s a spare, affecting story of a young nun in 1960s Poland, orphaned during WWII, and learning of her painful Jewish family history as she prepares to take her vows.

I caught up with it over the weekend, and was thrilled by its own elegant composure and wry writ — but what makes it doubly gratifying is the creative recovery it signals for Pawlikowski, a wonderful filmmaker who made a splash in the early 2000s with “Last Resort” and the BAFTA-winning “My Summer of Love,” before his wife’s untimely passing put his career on hold. Last year’s drab Paris noir “The Woman in the Fifth” wasn’t the comeback we were hoping for; “Ida” certainly is, and this win validates it. Pawlikowski seemed surprised to be accepting the award, singling out “Under the Skin” as he enthused over the standard of competition. (Meanwhile, I overheard French saying the choice had been a very easy one.)

For the record, “Ida” joins previous Best Film winners “A Prophet,” “How I Ended This Summer,” “We Need to Talk About Kevin” and “Rust and Bone” — the prize is five years old and has yet to hit a dud choice.

The festival’s oldest prize, the Sutherland Award for Best First Feature, went to Anthony Chen’s touching Singaporean family drama “Ilo Ilo” — beating such competitors as “Kill Your Darlings” and “Salvo.” The win echoes the young director’s Camera d’Or triumph at Cannes; it may be one to keep an eye on in the Oscar race for Best Foreign Language Film, where it is Singapore’s official submission. Further thoughts in my review here.

Going into the evening, the favorites for the Best British Newcomer award appeared to be the two brilliant child stars of “The Selfish Giant,” Conner Chapman and Shaun Thomas — though once juror and comparable veteran Saoirse Ronan took the stage, we were told that the jury had found it too difficult to separate them. The boys settled for a Special Mention, as first-time screenwriter Jonathan Asser took the award for ferocious prison drama “Starred Up.” The industry novice, who based the script on his own experience as a prison employee, noted with a smile that “it feels funny to be a newcomer at 49.”

Finally, the Grierson Award for Best Documentary went to Austrian director Paul-Julien Robert for his riveting, highly personal doc “My Fathers, My Mother and Me,” in which he unsparingly recounts his experience of growing up in a sex commune rife with psychological abuse — and demands difficult answers from his stricken mother. An unusual and necessarily uncomfortable film, it was a highly popular winner — judging from the whoops that greeted its announcement — even in the face of such acclaimed opposition as Frederick Wiseman’s “At Berkeley,” Alex Gibney’s “The Armstrong Lie” and Cambodian Oscar entry “The Missing Picture.”

To recap:

Best Film: “Ida,” Pawel Pawlikowski

Sutherland Award for Best Debut Feature: “Ilo Ilo,” Anthony Chen
Special Mention: “B For Boy,” Chika Anadu

Best British Newcomer: Jonathan Asser (screenwriter), “Starred Up”
Special Mention: Conner Chapman and Shaun Thomas (actors), “The Selfish Giant”

Grierson Award for Best Documentary: “My Fathers, My Mother and Me,” Paul-Julien Robert
Special Mention: “Manhunt,” Greg Barker; “Cutie and the Boxer,” Zachary Heinzerling; cinematography of “Pipeline,” Alexandra Ivanova