At least the Motoring Heritage Centre has and web site, and one of the pages features the very staircase:
http://www.motoringheritage.co.uk/html/the_centre.html
Regrettably, this is the only part of the centre that looks like this, and the rest is just shop units and breeze block construction tacked on the back. It is worth wandering around the fire stairs and rear accesses though, as the modern build is integrated in parts with remaining pieces of the original structure, which can still be seen:
Couldn't recall exactly what its wartime duty was, but this reminded me that its task was the construction of torpedoes.
When built, around 1905, it was the biggest car factory in the world. By 1910, it was non-profitable, turning out only 452 cars, half the number needed to break even.
Grade A listed, the restoration cost was around £6 million.