I've been into that building
the exchange itself is, I believe, on the first and second floors, the rest of them being occupied by some chunk of BT's other operations (I have a feeling it might be wholesale, but I wouldn't swear to it). There are doors into the exchange area served by the main stairwell, which also includes a lift shaft, which comes out at ground level into a teensy reception area directly behind the door into Farm Street, which is next to the pub. The street itself is VERY quiet even in the middle of the day, to the extent that there's a sign on the inside of the door saying something to the effect of "Please don't slam the door, it pisses the neighbours off". I didn't make a detailed survey of the security measures.
Anyway, the upshot of all this is that I would very strongly suspect an inside job: it really wouldn't be that hard to get a few mates in through the front door, set about the hardware, lump it back out to a waiting BT van and make good your escape.
Coat as in helping oneself to the contents...