The university also considers that there is improper motive behind the request.
What a coincidence! I consider there's an improper motive behind their refusal.
Seriously though, they get to decide what someone else's motive is, and act on that?

Judge, jury, and executioner kind of thing?
Coyne's request was completely legit. It's too freaking bad they don't like their perception of his motives. That shouldn't alter the fact that by publishing in PLOS, they agreed to release the data. The rules don't say, "You must release the data upon request unless you decide the motive of the requester is improper." Sheesh.
The university considers that this request has caused and could further cause harassment and distress to staff.
Speaking as a published researcher, I can say in full confidence that releasing data cannot cause distress to the study authors unless the data has been deliberately falsified or falsely reported. Okay, I suppose if the work is just extremely poor without intent to mislead, the authors could be subject to embarrassment, which would be distressing in a way. But that is certainly no excuse for not releasing the data.
Good research stands up to scrutiny. Poor research may collapse under scrutiny, but that's the way science works. You're not supposed to say, "No, you can't look because I'm embarrassed at the quality of my work." You're supposed to suck it up and deal with the consequences of your actions.
What a bunch of whining babies! Grow up and act like real scientists. If releasing your data is going to distress you, well, put on your big boy or girl panties and face the truth. You made the mess, now you are going to have to deal with it.
This whole thing is incredibly shocking... from the appalling misinterpretation of the data that we can see to the refusal to release the data while giving ridiculous and whiney excuses. QMUL should be ashamed of itself.