I am of the generation that grew up believing that Robert Powell was Jesus. This is because in my day you knew Easter was around the corner not because of the bastardised diffusion lines of Creme Eggs infesting the supermarkets (White chocolate? Caramel? Come on!), but because the TV schedules suddenly filled with truth ’n’ resurrection-based programming, central to which was the annual showing of Franco Zeffirelli’s four-part 1977 series Jesus of Nazareth. Powell played the Messiah and anyone else who was anyone in 1977 (Laurence Olivier, Christopher Plummer, Anthony Quinn, Ernest Borgnine, Rod Steiger, Peter Ustinov, Michael York, you name it) played the rest of the cast of the Bible. It was as much part of the season as making palm crosses at school or egg-hunting in the garden.

It is possibly still available somewhere out there in the fragmentary world of streaming, if you want to unearth it from underneath the secular detritus at a suitable moment. But it’s not the same as when it’s featured in terrestrial TV’s regularly scheduled seasonal programming.

On the face of it, Pilgrimage: The Road Through the Alps looks like a shoddy attempt by the BBC to fulfil some embarrassing clause lingering in its public service remit. Seven celebrities of different faiths and none are sent off to walk and bus the 190 miles of the Austrian Camino, a revived medieval Catholic route that finishes in the foothills of the Swiss Alps. Together, they see what they can learn about themselves, about faith and about medieval Catholic fortitude as they try to imagine crossing the Alps in the days before Gore-Tex and Craghoppers.

But – a miracle! Pilgrimage quickly reveals itself to be not too bad and, before the three episodes are up, you could be moved to call it really quite good and admit that the whole experience has, against all odds and expectations, been rather uplifting.

Mostly, this is down to the fact that all the pilgrims take it seriously – not sombrely, but seriously – and are willing to talk honestly and thoughtfully about what God and religion mean to them. No artificial timeline has been imposed on their trek – this is not an unseemly race from Innsbruck in Austria to Einsiedeln Abbey in Switzerland but a genuine (yes, yes, within the constraints of a programme still needing to be made) chance for the group to get to know each other, reflect on their past and current experiences, be influenced by each other and deepen rather than cheapen their thoughts. And there is no engineered conflict. In fact, no conflict worth the name at all. It is striking and rather wonderful.

The Wanted singer Jay McGuiness was raised Catholic but now describes himself as agnostic. He is, he says, still searching for the catharsis faith once gave him. And he is still grieving for his bandmate Tom Parker, who died three years ago from a brain tumour, brutally young and brutally soon after diagnosis.

Harry Clark (former soldier, second winner of The Traitors and, according to his mum “the smartest dumbest person … I’m just wired backwards”) is a fellow Catholic, who still believes. But he seems almost more entranced to be in the company of people talking about history and ideas as they yomp along than by the possible presence of the divine at the various ancient monasteries and convents they visit.

Comedian Helen Lederer is feeling the pull of her father’s Jewish heritage and the unspoken grief her family carried. “But you don’t want to overclaim it,” she says, as she tries to feel her way along the boundary between the effects of trauma and experiencing the trauma yourself. Again, a rare subtlety in such shows, in which overclaiming is virtually a requirement.

Paralympian Stefanie Reid has a strong Christian faith, born of the accident that nearly killed her and led to her becoming an amputee in her teens. Comedian Daliso Chaponda (further marking the documentary out from the herd by being naturally funny and thoughtful by turns, instead of a relentless joke seeker and teller), who grew up in 14 countries as the son of a refugee, has sampled a number of Christian denominations and is hoping to find one that truly feels like home.

Journalist Nelufar Hedayat’s Muslim family came to the UK as refugees from Afghanistan when she was seven. She is struggling with the anger she feels towards Islam and how to unpick a religion from its cultural expression and enforcement by – for example – the people who are, in her native country, forcibly silencing women.

There is, by the end of three episodes – which are full of the most gorgeous scenery, and I will take a travelogue too, if anyone is listening – actual growth and learning. As a committed atheist, it didn’t bring me any closer to God, but it may just have renewed my faith in celebrity documentaries.