Has a tiger come to tea at the Lupus film studios? No, but an equally disruptive guest has turned up. There are dozens of people beavering away on each floor of this smart London townhouse – animators, producers, artists – when my two-year-old daughter Romy arrives for a sneak preview of what they’re working on: an animated version of Judith Kerr’s beloved children’s book, The Tiger Who Came to Tea, which turned 50 last year.

Providing a rampaging toddler doesn’t accidentally unplug all their computers, the animated story of Sophie, Mummy and the unexpected stripy visitor who eats and drinks them out of house and home will air on Channel 4 on Christmas Eve. But rogue two-year-olds are not all the team has had to contend with.

Three months ago, says producer Ruth Fielding, the colouring process was proving so time-consuming she doubted they had the money or time to finish it. The swift recruitment of 20 students from Middlesex University solved that problem. There was also trouble over a scene from the book that shows the tiger picking up a teapot and pouring scalding hot tea straight into his mouth. “We had to add a line for Mummy that says, ‘Be careful, it’s a bit ... hot!’” says Fielding. “It makes for a comedic moment, but it was actually borne out of Channel 4 worrying that it could be classed as imitable behaviour.”

There was also, more sadly, the death of the story’s creator, aged 95, in May. Kerr had been very involved: advising on the script, approving the cast, even chipping in on the precise shade of red used for Sophie’s coat. And, before all this, Lupus first had to convince Kerr they were the right people to bring her story – which has sold more than 5m copies – to the screen. The hand-drawn aesthetic that made their version of We’re Going on a Bear Hunt such a treat helped their case, while the fact that Kerr was allowed to weigh in on the film was doubtless another factor.

“Initially, there were a few more lines for the tiger,” says Robin Shaw, the director. “She wasn’t having any of it – and she was bang on. The Tiger only says two things in the book, but you don’t ever feel he’s lacking in presence or character. The minute you put words in his mouth, he becomes someone else.”

Shaw hit it off with Kerr: they’d talk endlessly about pencils, lines, the use of perspective. He remembers telling her how clever it was that the Tiger’s eyes are always perfectly aligned with the vanishing points and the focus of the page.

“And she said, ‘Oooh, really? I didn’t realise I’d done that.’” says Shaw laughing. “It was all natural for her.”

Was it hard to carry on after she died? “Of course it was sad she wouldn’t be there to see it finished. But, in a strange way, it was motivating– it made us want to do an even better job.”

It’s time to take a tour of the building. Romy has been temporarily distracted by a tea party the team have put on for her, so I sneak out with line producer Adam Jackson-Nocher. He shows me a vast storyboard pinned along the corridor, with each panel colour-coded to show where they’re all at. It’s head-spinning stuff. There are 20,000 individual drawings – all needing sketching, tidying, colouring and finessing – to make this 24-minute film. Technology plays a part – a nifty brush has been designed to paint instant furry tiger stripes – but for the most part it’s drawn by hand.

The team talk me through a scene where the “camera” is looking down from the ceiling, spinning around as buns tumble towards the table. Computer-generated animation would speed things up here, but it would also give everything a consistent “correct” look – and that is not how Kerr drew the book. Entire kitchen units would change or even disappear with a turn of the page, depending on how Kerr wanted things to look.

To make this charming inconsistency work, an 80-strong team had to draw under strict guidance, each fully understanding not just how the tiger should look but how he moved and what sort of character he was. “He’s the Roger Moore of tigers,” shouts Shaw from across the room. I laugh but it turns out he’s serious: “He breezes in, affects everyone’s life, manages to get exactly what he wants, then breezes out again leaving everyone feeling kind of used but happy with that. He’s a seducer, a charmer. He’ll only do something if he wants to, and will only give something if it looks like he might get something in return. Completely selfish, but in the nicest possible way.”

It’s time to test the magic, so we head back to the tea party room for a screening. Things get off to an unpromising start when I walk in to find Romy ignoring the biscuits and fruit juice in favour of playing with the office’s fancy Fortnum and Mason china tea set. I clench my teeth as she bashes the delicate cups together.

Then – just as I’m cursing myself for breaking the golden “never-bring-your-child-to-work-unless-you-absolutely-have-to” rule – the screen catches her attention. Seeing the characters she’s grown to love come to life mesmerises her, even though many have still to be coloured in. Occasionally, they disappear altogether, to be replaced by handwritten notes. Despite this, it’s clear the story hasn’t lost any of the warmth of Kerr’s original. The tiger retains the slight edge of menace that makes him so captivating, and there’s excellent casting in the voices of David Oyelowo (Tiger), Tamsin Greig (Mummy) and Benedict Cumberbatch (Daddy).

To turn this very short story into nearly half an hour of animation has involved a bit of licence, most notably the addition of a glorious musical interlude sung by Robbie Williams, who fell in love with the book after reading it to his daughter, Teddy. Again, Kerr had an input into this musical passage, suggesting that its references to such foods as pizza were replaced by more traditionally British items, such as ice cream and chocolate cake.

Most people who have read The Tiger Who Came to Tea will have a favourite illustration. For many, it’s the evening scene after Daddy comes home and, realising there’s no food left in the house, takes Sophie and Mummy out to a cafe. Sophie is dressed in her nightie, coat and wellies, but just behind her sits a stripy, ginger cat in the glow of the street lights. For Fielding, one of the animation’s key illustrations isn’t actually part of the story – instead, it features on the inside sleeve of some versions of the book. It shows Sophie and the tiger drinking lemonade together through straws.

“There was a bit of a eureka moment when we were writing the script because we realised that Sophie could imagine what it would be like if the tiger stayed for ever. So she recreates him going to school and sitting on her bed, then comes to the realisation that actually it would be ridiculous – you can’t have a tiger at home. Judith responded really well to this idea, meaning we’re not confined to the four walls of the house.”

Indeed, if the book itself is about one thing then it’s imagination. The huge amount of white space on almost every page invites readers to let their own minds run free. Perhaps this is why the story lends itself to so many different readings, from feminist ones (is the Tiger the male of the house who does no housework?) to Michael Rosen’s notion that the stripy visitor is an intruding Gestapo officer. (Kerr grew up in Germany but the family fled to Switzerland and then Britain as the Nazis closed in.)

When we first read the book to Romy, my wife was pregnant with our second child and it was hard to avoid the metaphor: here comes a new guest to upend the nice time you had planned with Mummy. But Kerr always insisted the story be taken at face value, that it’s about a child’s most wonderful fantasies. Romy’s reaction is testament to that – and ever since she’s seen the tiger slinking around the screen she hasn’t stopped wanting him to come for tea.

• The Tiger Who Came to Tea is on Channel 4 on Christmas Eve at 7.30pm.