Why?
It's political self-interest. It's a "news" story, gets him a bit of positive coverage and as the original event is 50 years in the past, it can't possibly stick to him as having any culpability in the first place.
Yes, it's good Turing finally got an apology and I'm delighted, if it's just several decades late. And we can't even really blame other governments for not having acted earlier as I doubt many if any in government even knew about it before this campaign.
We can't even really blame the government at the time, as to do so, we'd have to judge by our own standards of today and they didn't have those standards.
Turing was a great if largely (publicly) unrecognised thinker, up there (
IMHO) with the Isaac Newtons, Brunels and Einsteins of their respective times, made a significant contribution to the war effort in WW2 (the size of which we'll probably never really know, but a lot of people probably owe him their lives without ever knowing it), and what happened to him was horrible. But it was a symptom of standards of the times, and I'd bet both my nuts that we, today, are doing things that future generations will look back of with dismay and disgust, because their standards will be different to what we accept as the norm.
But Kudos for Brown? I don't see it. This move is all political upside, carries a zero political cost or risk, and is a political no-brainer. It's a bit of a godsend for him that he can find a way to get in the news when he's not at the pointy end of criticism or controversy, be it over one hot potato or another, or his inept economic management. He must have thought his birthday and Christmas have all come at once this year.