Heller imaginatively sets up this premise at the start. The film begins with Hanks recreating the television show, walking in the door as Mr Rogers did every time, putting on his signature comfy red cardigan, and singing the theme song, Won’t You Be My Neighbour? But after presenting a picture board with characters from the programme, he comes to a photo of Lloyd, his face bloodied. So much for any hint of sappiness or escapism. From there the film moves smoothly into Lloyd’s story, including the fight with his father, and the Esquire offices where he reluctantly agrees to talk to that kids’ show guy.

Hanks gets Rogers’ mannerisms just right: the sweet half-smile; the slow and precise manner of speaking. But he doesn’t coast on mimicry or his good-guy image. This is a rich and subtle performance, in which Hanks makes Fred Rogers’ sincerity completely convincing and real. When Fred turns Lloyd’s questions back on him, Hanks lets us see that the reaction is partly defensive but also based on genuine curiosity and care for other people. Rogers has such clarity about others and such a gentle way of guiding them out of their problems – never a harsh judgement from him – that by the end of the film he has come to seem like the world’s best therapist.

The relationship between Fred and Lloyd is emblematic of the many friendships that Rogers, who died in 2003, cultivated in his life and during the remarkable 33-year run of his show. That friendship is so much the centre of the story that the film leaves Fred for long stretches to follow Lloyd. Rhys matches Hanks in creating a deeply believable character, whose trajectory from furious cynic to forgiving son could easily have been either overacted or oversimplified. Rhys’s tough-minded performance reveals the hurt that has kept Lloyd so angry. Cooper is dynamic as Jerry, something of a boor, but also a man who is making a last, desperate attempt to reach his son. (That Lloyd is grappling with his estranged father and new son at once is among the screenplay’s few overdone elements.) Susan Kelechi Watson brings a loving and witty edge to Lloyd’s wife, Andrea, who responds to his scepticism about Mr Rogers by saying, “Please don’t ruin my childhood”.