I am a fan of Agatha Christie perhaps because one of my early and formative theatrical experiences involved going to see And Then There Were None at a little theatre in Somerset. I remember the warmth of the summer evening, the stiffness of the chairs, the sense of walking into an enclosed, other place where you were going to be told a story. It felt like magic and has stayed with me ever since.

Which is why I went with a spring in my step to this revival, directed by the talented Lucy Bailey, of the 1953 West End hit Witness for the Prosecution – recently adapted on the BBC to gripping effect. An added bonus was the setting: like most people I've never seen the now-disused council chamber at London County Hall on the Southbank.

It was indeed fascinating to glimpse inside this grand building. Its towering pillars, rich wooden seating and gilded circular ceiling do on the surface of things seem the perfect place in which to stage a play that spends a great deal of time in the Old Bailey, as Leonard Vole is put on trial for the murder of an older, wealthy woman he has befriended. In William Dudley's design, a model of the statue of blind Justice, holding her scales, hovers above the judge's bench to remind us of that fact. Members of the audience are roped in to play the jury.

The trouble is that not all of Witness for the Prosecution takes place in court, and the cumbersome nature of the space mitigates against swift scene changes. People trundle in with rolls of carpet and tables and chairs, but it all amounts to a sense of clunkiness that Christie's own script does nothing to dispel.

The plot relies heavily on the incredible, but is clever. If you don't know it, its twists still have the capacity to produce gasps of surprise. Yet the writing is old-fashioned in the extreme, repeating things we already know and then rushing through elements that are new.

Bailey keeps things chugging along, but can't solve the essential inertia. Her cast plug away energetically too, but only Philip Franks and David Yelland as the two opposing barristers catch the right tone; they are both serious and slightly knowing, pulling the maximum effects from their lines. But Jack McMullen is too gauche for Vole and Catherine Steadman as his wife Romaine is too shrill and stompy to convince. A disappointment.

Witness for the Prosecution runs at London County Hall until 11 March 2018.