MALALA Yousafzai and David Letterman are standing in Oxford University’s souvenir shop on High Street.

The talk show host, one of the most famous men in America, is trying to persuade the 20-year-old Nobel Peace Prize winner to let him buy her an Oxford University jumper.

She doesn’t want one. She tries gently to tell him so, but the bearded Letterman won’t have it: he insists, then he also makes her pin a souvenir badge of her college onto his lapel and declare him an honorary student.

It’s not a comfortable scene, and it’s one of many uncomfortable scenes in a 50-minute-long programme – the latest episode in Letterman’s new Netflix show, My Next Guest Needs No Introduction.

As well as a sit-down interview recorded in front of a live audience in Letterman’s native New York, the show cuts to clips from a trip he made to visit Malala at her new home: Lady Margaret Hall, Oxford, where she enrolled in September.

It even includes a clip of Letterman having a fish and chip lunch (which he bizarrely eats with his hands) with Malala’s father Ziauddin Yousafzai at the Rose and Crown on North Parade.

The show actually begins with the six foot-tall Letterman gatecrashing Malala as she gives a guided tour around her college to a group of prospective students, which is the show’s way of revealing that in between studying on her PPE course (the famous Politics, Philosophy and Economics degree long favoured by prospective politicians including David Cameron) Malala has signed up as a college tour guide.

She also reveals that she has joined a cricket club in Oxford – which makes perfect sense given her Pakistani background – and has been taking driving lessons.

When asked about her social life, she offers a reassuringly human reply: “In Oxford there’s a lot to read: you get a lot of work and assignments so you have to keep that in mind whatever you do.

“Every day I’m busy doing something with my friends then I remember I have an assignment to do...”

For the most part, she deftly bats away Letterman’s juvenile japes like an irritating wasp.

At one point during the New York interview, Letterman asks with evident satisfaction: “So what do you think about president Trump?”, like a child who’s just asked the teacher if she knows what coitus means.

Malala calmly retorts: “Well I’m in the UK, so what do you think about him?” to whoops of delight from the audience.

If Letterman was hoping to get the sort of political mudslinging he was used to from guests on the Late Show, he is disappointed.

At the souvenir shop he asks her if she is planning to go into politics, and she reveals that is not the plan – at least not as a member of Parliament.

After Oxford, she says, “I want to finish my course then continue my work for girls’ education... I want to see more girls getting education, getting empowered and becoming the leaders of tomorrow.”

For Malala, it becomes clear, Oxford is not a means to an end – it is the end: for the girl who took a bullet in the head standing up for girls’ fundamental right to go to school, education itself is the goal.

Attending Oxford University was never about opening doors – as it is for so many.

Elsewhere in the programme, she talks about the schools she is already helping to build in deprived areas around the world.

Her main goal, she reveals, is not to be a leader, but to empower others to lead their communities.

“There are other young girls out there, if we give them support they can raise their voice and change the world.”

Over fish and chips at the Rose and Crown, Malala’s father offers another perspective on his daughter’s time at Oxford.

“With her very existence now I can feel she is making a big change in the world,” he says.

One of the most inspirational moments in the show comes, not surprisingly, when Letterman asks Malala whether, having survived being shot in the face, she felt her life was being guided by a higher purpose.

She thinks for a while, then replies carefully: “I think there might be... but even if there isn’t, you yourself can make a decision.

“When I woke up and realised I’d survived such a brutal attack, and saw death so close, I realised maybe this life is for a purpose, and I decided I’d give this life to girls’ education and speak out for them.

“My goal is to do as much as we can to help others.”

As far as being an inspiration to the next generation goes, her mature and unflappable handling of the hyperactive and provocative talk show host isn't a bad start.

Malala 1 – Letterman 0.