The language Trump uses is really troubling and what the Labour are doing is horrific,” says the political satirist-turned playwright Henry Naylor when we sit down to talk about his play Games.

“It’s a historical piece based on two German Jewish athletes who were at the top of their game and who the Nazis tried to exclude from competing in the 1936 Olympics. Hitler wanted a purely Aryan team,” explains Naylor. Formerly the lead writer of Spitting Image, these days he’s a playwright of what he calls “humanitarian” plays. His Arabian Nightmares trilogy was about the Middle East in the 21st century including the war in Syria. But Games explores today’s themes by looking into the past.

“The Americans were really set against coming to the games,” he continues. “There was a really strong boycott movement against them. So the Olympic Committee went to Hitler and said “’find some Jewish athletes.” Hitler said there were none good enough and the American public said wait a moment, there is a girl who is German and Jewish who is studying in America at the moment, and who was the former Olympic gold medalist fencer. She’s probably good enough.”

Helena Mayer was an international sporting celebrity at the time. And at the same time another athlete called Gretel Bergmann was an up and coming star, whom nobody had heard of. The Nazis tried to exclude her even though she was a fantastic high jumper. They gave her the worst possible facilities, and wouldn’t allow her to compete against Aryans. But it spurred Bergmann on and in the run-up to the Olympics she broke the European record.

According to Naylor, Bergmann’s performance forced the Nazis to make her part of their Olympic team, but withdrew the offer once they knew the American team were on the boat taking them across the Atlantic. Mayer, was able to compete because she was not only a famous Olympian but because she had “perfect Aryan features.” So does the Jewish actress who plays her, Sophie Shad.

“It’s really funny in that I’m Jewish but I am hardly ever allowed to audition for Jewish roles because I don’t look ‘typically Jewish’,” says Shad. “But I must look Jewish because I am Jewish!”

At 24, she brings a rare insight to the themes of Naylor’s play.

“I can connect with it, because my Hungarian grandfather was a Holocaust survivor. He was in Auschwitz and then Mathausen. He died when I was quite young but my dad has always made sure we knew about his father’s history.”

And there is another connection to the subject because Shad wrote, produced and acted in a film, Kitty’s Fortune, about her boyfriend’s grandmother, the well-known Holocaust survivor Kitty-Hart Moxon. Shad played Kitty in the film, an experience which must make the role of Helene all the more interesting, not least the scene in which she raises the Nazi salute.

But the salute didn’t quite mean then what it means now, explains Shad.

“Helena was half Jewish, half German and in quite a unique situation in that she had been a national treasure for Germany. I think she felt deeply German and people had statues of her on her on their mantlepieces. It was 1936 and a Nazi salute was not as sinister as it is for us today. It was the same with the swastika. So I’ve tried to do the salute with her mindset. When she salutes, the crowd roar their approval. And for one tiny moment she’s thinking ‘I could be a national treasure again.’”

“And what we forget is that at the time, I think the England football team gave the Heil Hitler salute in 1938,” adds Naylor. “Also Helene had family in Germany and you just don’t know what the implications would have been for them if she had refused the salute.”

“It does make me feel strange,’ admits Shad. “But that’s acting. You have to separate yourself.”

“Mayer has been kind of forgotten,” says Naylor “But in the late 20s and early 30s she was the David Beckham of Germany. She was massive. Young, beautiful and talented at a time when Germany had a crisis of identity, she was someone who showed the German public that Germany could be a force in the world again.”

For Naylor the idea for the play arrived accidentally while having a drink with the actress Avital Lvova while touring one of his Arabian Nightmares plays.

“She is Russian German Jewish and we were sat in a bar and I said ‘I’ve got to think of my next play. I should write something for you,’ says Naylor, an uncommonly tall Yorkshireman who isn’t Jewish but whose godmother was a refugee from Vienna. “And because Avital has the build of an athlete I googled: ‘German Jewish female athlete’ and then ‘Nazis’, and this story pinged up.”

A week into rehearsals for this newly cast run, Shad is already finding the play is having an effect — especially that Nazi salute.

“We performed it yesterday to 50 uni students and at the end they all said that that was a really powerful moment. They obviously know what it is weighted with.” For Naylor, the hope is that the play will help to thinking about politics today, and not just in Germany in the 1930s.

“When I wrote it a couple of years ago I put in lines like ‘making Germany great again’ and ‘draining the swamp of Weimar’. But I don’t think I would put them in now because everyone can see the relevance.” And yet he concedes that the lessons are not obvious to everyone.

“I’ve got good friends who are Labour Party supporters who are very blinkered to what’s going on. They say [about accusations of antisemitism in the party] ‘Oh, it’s just a conspiracy.’

“I just think everybody should be talking about antisemitism. Everybody should be getting it on the agenda and trying to stop it.”

Games is at the Arcola Theatre until December 22, with another of Henry Naylor’s plays, Borders