"The only thing necessary for the triumph of evil is for good men to do nothing." Edmund Burke's famous dictum might very well be the starting point for this riveting play which reveals how easy it is for evil to arrive on your doorstep and seem very plausible.

In Roland Schimmelpfennig's sharp and fierce depiction, he is a dignified old man called Rudolph who meets Corinna, a lonely older woman, on a snow-bound train on Christmas Eve. At her invitation, he arrives at the home of her daughter Bettina and son-in-law Albert and is soon seated at the piano, playing Bach and holding forth on the need for a fractured society to come together and remember old-fashioned values like chivalry, decency and create "a new world which will last for ever".

Schimmelpfennig is one of Germany's most prolific and popular playwrights and what is brilliant about Winter Solstice – translated by David Tushingham and given a scalding co-production by the Orange Tree and the Actors Touring Company – is the way it shows the seductive appeal of dangerous, neo-Nazi views, the ease with which it wins converts to its side. Written in 2013, in response to the re-emergence of the far right in Europe, it feels like a bellwether in the time of Trump and Brexit, a warning of just how easy it is for liberal values to be overcome.

The setting is a household, we are told, "where no-one has ever voted Conservative" and yet by the close the majority are under Rudolph's spell. Only husband Albert stands apart; he is a social historian, writing a book about Auschwitz and he knows exactly what he is dealing with. Yet politeness and social fallibility prevent him from speaking out. Evil has triumphed.

All of this makes Winter Solstice sound like a grim evening. In fact it is often devastatingly funny. This is your average dysfunctional family, where everyone is hiding their dislike of everyone else with the help of vast quantities of red wine. As they talk to each other, they also describe their actions, in long-intricately written stage directions that may be the basis of a film shooting script.

This combination often produces richly comic effects as when a character has to mimic an action already described – "she smiles a pained smile which she has seen in the cinema" – but also involves the audience intently in the story; you have to collude in its artificiality. The intimacy created is further underlined by Lizzie Clachan's design that places the actors in what looks like a rehearsal room, moving tables to create new spaces, and using unlikely props to stand for other objects. The building of a Christmas tree from pans and boxes is particularly effective.

Ramin Gray directs with energetic aplomb, although the tension slightly flags towards the end. And the acting is immaculate. Nicholas Le Prevost is attractive but menacing as Rudolph, Kate Fahy an eternally eager and perpetually disappointed Corinna, grasping at happiness with bright eyes. As Bettina, Laura Rogers catches exactly the right brittle note, while Milo Twomey is suitably slimy as the artist whose conversion to the cause is terrifyingly extreme.

And as Albert, a gentle man with his own sad secrets, a dangerous recklessness with heart tablets, and an unfortunate allergy to pine trees, Dominic Rowan becomes a comic, crumpled Everyman, someone who knows the truth but can't bring himself to tell it. Someone like most of us.

Winter Solstice runs at the Orange Tree Theatre until 11 February.