We have Pia Zadora to thank for the portrayal of Anne Frank by which all others are judged.

The benchmark was set, if you believe the hoary old tale, on opening night in Cleveland, Ohio.

The amateurish Zadora, who spent a month in rehearsal becoming progressively more wretched, insisted everything would be fine by curtain up. She lied.

So when a German patrol arrived on stage, and reached the door of the house where the Franks were hiding, an exasperated voice from the audience yelled "she’s in the attic".

It's probably an urban myth. But, needless to say, Ellie Kendrick is rather more convincing than Zadora in the role in BBC1’s vivid take on The Diary of Anne Frank (7pm).

This beautifully-filmed fresh adaptation is said to be the first to weave the actual words from the diary itself into a screenplay, and Deborah Moggach’s careful, faithful script is all the richer for it.

Kendrick is exceptional in the lead, delivering a naturalistic, nuanced performance that’s almost as precocious as Frank herself.

She’s funny, flirty and playful as well as unnerved, bored and stroppy, and has an uncanny ability to channel meaning with a mere glance.

Most dramas would count themselves lucky just to have her but the BBC have assembled a stand-out cast, including Iain Glen, as Anne’s noble, subdued father Otto, and Lesley Sharp, as the flighty, quarrelsome Mrs van Daan.

Yet aside from Kendrick, it’s Black Books’ Tamsin Greig who truly catches the eye. She’s terrific as Anne’s shellshocked mother Edith, whose haunted face conveys the fathomless misery beyond the annexe and leant depth and context to the opening episode.

"Father says I should be nicer to her," says Kendrick’s Anne, in a conspiratorial voiceover, "but sometimes I want to slap her across the face."

That’s one of most engaging elements of the world according to Anne. Even with jet-black reality pressing in, she remains an ordinary girl, with an ordinary girl’s concerns.

There are no prizes for guessing what happens in the end, of course. But this is a fine production by a broadcaster on top of its game.

With anti-Semitism once more flaring up like a nasty rash, this strangely scheduled drama – which plays out in a soap slot over the course of the coming week – should be required viewing for schoolkids. And, for that matter, licence fee naysayers.

If nothing else, the next few nights should provide a blessed bit of perspective whenever the Celebrity Big Brother inmates start grumbling about their lot.