Somewhere, perhaps hidden behind a pillar on one of the floors of this disused building in Shoreditch, there lurks the perfect version of Mincemeat just waiting to be told in all its gripping simplicity.

Unfortunately, what Cardboard Citizens, that admirable professional company working with ex-homeless people, has for us in this promenade production is the decidedly flawed version of the narrative, with all its baggy frustrations.

The first 45 minutes, along with some pointless promenading, could easily be cut.

As it is, we have to plough through bewildering scenes of anarchists kidnapping a judge and the cast wittering about Hitler in a hostel in 1909 before the main thrust is belatedly revealed by writers Adrian Jackson and Farhana Sheikh.

What a thrust it is. In 1943, British intelligence devised Operation Mincemeat, in which the carefully dropped body of a dead British soldier would conceal documents designed to fool the Germans about the Allied invasion plans for mainland Europe.

Winding up thrillingly in a wonderfully recreated communal WW2 shelter, we walk through a number of scenes, piecing together fragmentary details both about the operation itself and the wretched life of the so-called Major William Martin, an unsung hero of the war effort whose personal situation chimes with this company’s concerns.

Ifan Meredith looks suitably wracked as Martin and there’s a nice through line in wartime bonhomie, even if the acting overall tends to the broad.

It’s hard, though, to comprehend how Jackson, also directing, didn’t spot how this ideal subject matter is overplayed and ponderous when it should be brisk and slick.

Until 12 July (020 7478 0100, www.sohotheatre.com)