Hotfoot from a three-week stint at the Edinburgh Festival Fringe, the Oxford-based theatre company Idle Motion are back on home territory for their first performance at Oxford Playhouse.

The group, which is composed principally of former pupils at Cherwell School, is performing That Is All You Need to Know, its 80-minute study, in its trademark visual and physical style, of the brilliant code-breaking operation at Bletchley Park that gave a crucial advantage to the Allies during the Second World War.

This is one of two shows the company took to Edinburgh. The other was a revival of its earlier success, Borges and I, exploring the life and writing of Jorge Luis Borges (1899-1986).

In the last week of the festival, they were performing both shows on the same day. This proved an arduous task, as founder member Kate Stanley told me in a telephone call from their shared Edinburgh home — “especially since we’re trying to see a show by someone else every day as well”.

Kate said she and the team were eagerly looking forward to treading the boards at the Playhouse where they have been associate artists for the past three years.

“We all grew up here,” she said, “and it was the main space that we went to see work when we were children. It is going to be an emotional experience.” Idle Motion had its origins in shows staged by the members of the group in their days at Cherwell School. These were created under the supervision of its head of drama Paul Slater, who has continued to work with the company in every show since. Its principal members, besides Kate, are Ellie Simpson, Grace Chapman, Sophie Cullen, Christopher Bone, Joel Gatehouse and Nicholas Pitt. Technical matters, including lighting and sound, are handled by Greg Cebula.

Having got together on a more permanent basis after university (Kate studied drama at Exeter), they began working on multi-media shows that were and remain a collaborative venture in all respects. One of their first successes in 2010 was The Vanishing Horizon, which dealt with female pioneers of flight. This was seen in Edinburgh and around the world in a British Council-sponsored tour that visited countries including China, Malaysia and Taiwan.

The group’s interest in Bletchley Park was sparked by their learning of the troubled genius Alan Turing, who is played by Christopher Bone. One of Bletchley Park’s greatest minds, he is widely considered to be the ‘father of computer science’.

Turing was convicted of a homosexual offence in 1952 and subjected to chemical castration. He tragically committed suicide with cyanide two years later — a part of his life addressed in the show. The government recently signaled that it is prepared to support a bill that would grant Turing a posthumous pardon.

“What a fantastic life of achievement he had,” said Kate, “and what a sad ending.”

But rather than merely commiserate, the show is a celebration of what was achieved, both by the code-breakers themselves and those who later worked to save Bletchley Park from destruction and turn it into a museum and heritage attraction.

“There were so many people at Bletchley whose achievement hasn’t really been fully recognised,” Kate said. “This is because the thousands of people there who were not able to talk about their work at the time and for 30 years afterwards. This meant that sometimes they were branded cowards by people who had no idea of the vital job they were doing.

“Bletchley Park was able to put us in contact with some of these people and their stories are woven into the show.”

When it was performed at Oxford’s North Wall in May, The Oxford Times’s reviewer Angie Johnson succinctly summed up the play’s appeal in giving us verbatim testimony from the very people who cracked the Enigma code — extraordinary people whose quiet work changed the course of our history.

She wrote: “The play not only evokes the isolation of service life at Bletchley but also the cricket games on the lawns, bops at the village hall and jaunts up to the West End.

“As noted in previous productions, these agile performers never hesitate to tackle a big story. That Is All You Need to Know is a gripping and taut piece of theatre worthy of its subject.”

Oxford Playhouse

Thursday at 8pm

Box office: 01865 305305, oxfordplayhouse.com