They have strong evidence that he collects child abuse images. Even without proof, they could probably charge him with sinking the Titanic and still get a conviction.
They either have some form of evidence (even circumstantial like browser history, cache data or URLs gathered by the ISP via the usual inline proxies) or they have nothing at which point they won't be able to progress.
Do not underestimate the sheer hate that is directed towards this particular class of criminal. The inability to actually prove guilt is widely regarded as letting them get away on a technically.
Although I am personally of the opinion that people engaging in child porn and certainly those engaging in abuse should be strung up by specific body parts to the point of them separating, I still prefer to see due process - that's the law. As a matter of fact, I would actually prefer everything was done absolutely right so someone who would be convicted based on evidence would not stand a chance on appeal, also because it lessens the possibility of entrapment (CP laws are notoriously weak on prevention of their abuse, to the point of it being suspicious).