I can only guess. It could mean someone took their turn in connection with somethin, but it could also be using turn as in "taking a turn for the worse". Since there are no "turns" that I can think of that relate to 5 eyes, I am leaning towards the latter, and someone has taken a turn for the BETTER, which is why we have everything.
That confused me, too. But your explanation makes SO much sense.
I think it means someone in the UK who is involved is now cooperating for the first time.
Somebody important flipped. And the server can confirm what they have to offer.
I suppose it is worth mentioning Turn: Washington's Spies, a 2014 television series on AMC, which takes place during the American Revolutionary War... I do not know the specific source of the word 'turn' in this context.