It is surely a truth universally acknowledged that there are too many panel shows. It was already obvious a decade ago the world didn’t really need any more of them. So the arrival of Would I Lie to You? in June 2007 didn’t exactly feel like an auspicious TV moment. But every now and then, a show’s format and personnel dovetail precisely to create television that simply works and keeps on working. Would I Lie to You? is now a perfectly pitched, tonally surefooted BBC institution; as satisfyingly predictable and reliable as fish and chips on a Friday evening.

Like most TV institutions, it could easily have been a very different show. Alan Carr turned down the captaincy slot that was subsequently offered to David Mitchell. Also not quite right was original host Angus Deayton – Would I Lie to You? is a cheerful, open-hearted affair that Deayton’s inveterate smugness never really suited. The show hit its stride when Rob Brydon came on board in 2009. Daft and game but wry and knowing, Brydon’s tone was the perfect fit. And his gift for mimicry has meant he’s also become an excellent puncturer of the two team captains’ egos which, let’s be honest, do occasionally run wild.

As with so much of the most resonant British TV, at the heart of Would I Lie to You? is a relationship built around class difference. It is at the core of Lee Mack and David Mitchell’s counterintuitive comic chemistry. It’s north v south. Working men’s club v Footlights. Bob the Builder v Professor Yaffle. Mack and Mitchell both understand this and have accentuated their personas accordingly to the point where they’re now like a cranky old married couple; staring across at each other in a spirit of cheery antagonism, finishing each other’s gags. It feels like the most charming depiction of Stockholm syndrome ever seen on television.

Of course David Mitchell had a bell which he rang to summon his parents when he needed more orange squash … Mitchell with Rhod Gilbert and Miranda Hart. Photograph: BBC/Brian J Ritchie/Endemol

Their differences are the source of the hilarity, as with any great double act. Mitchell plays the effete Oxbridge hoity-toity to perfection – it’s somehow completely unsurprising to learn that as an infant, he had a small bell which he rang to summon his parents when he needed more orange squash. Mack, meanwhile, is self-consciously earthy and deflating, approaching the game like poker; quick-witted, unpredictable and slightly provocative. Mitchell interrogates, often with stagey rage. Mack rolls his eyes and takes the mick. As a good cop/bad cop team, they’d be unbeatable.

Like all the finest panel shows, Would I Lie to You? brings out the best in its panellists, sometimes to a surprising extent. You may not have pegged Gabby Logan as a comic but she more than holds her own here. Kevin Bridges’ standup might not generally stretch the boundaries of the medium but his story about the Bulgarian horse he and his friend may or may not have hired on holiday was a masterpiece of comic timing and misdirection. Bob Mortimer, meanwhile, is given the floor for a good third of any episode in which he features, rolling out his joyfully absurd selection of shaggy dog stories, true stories that sound like shaggy dog stories and odd, unexpected talents. Can Bob cut hair? Did Bob own a pet owl? Can Bob tear an apple in two with his bare hands? All these questions have surprising answers.

Can Bob cut hair? Did Bob own a pet owl? … the joyfully absurd Bob Mortimer with Lee Mack. Photograph: Brian Ritchie/BBC/Endemol Shine UK

Brydon is key here – he’ll edit or allow, cajole or indulge. He’s our guarantor of quality and his instincts are generally spot on. Because the show feels so natural, guests with constructed personas rarely cut the mustard. For example, Diane “Philomena Cunk” Morgan struggled to make an impression, because the show’s identity was stronger than hers. Ironically, you cannot lie to Would I Lie to You?

Would I Lie to You? is not the kind of show that will ever set critics’ pulses racing. Even so, it’s reached its tenth anniversary for a reason. It’s barely changed since Brydon took over the host’s chair and why would it? It’s not broken; there is nothing to fix. It could well lurk in the early evening schedules for another decade yet. We will still be vaguely willing to believe that Lee Mack once rescued a donkey from a holiday camp toilet, or that David Mitchell had a picture of Margaret Thatcher on his childhood bedroom wall. Because it’s part of the furniture now.