I'm gonna bend the rules a bit and approach this question from a different angle. Does it matter? How did they show what he was watching?
Since they recorded him with his own webcam, how would they know what he was watching? Sure, they can also record his screen but then they would have to compose both streamings in a single video, and that would be suspicious and/or easily deniable. How do you prove he was actually watching that and is not something you just added in editing?
Sure, some neighbours would actually believe anything they see and may not listen to reason or explanation. We know neighbours love a gossip, and ostracising feels so good and self-rightous...
Sure, his ISP could share his network activity if solicited by the police (I don't know the laws regarding that in the actual UK, much less in the fictional UK setting where the episode is set)
It is supossed to be a big twist at the end:
Alex: [The director] James Watkins kept giving me gentle nudges, reminding me how high the stakes were for Kenny. The audience might be thinking, "Oh, come on. You haven't done anything that wrong." And then we find out exactly what he has done.
But as shown in the episode it still seemed weak. They move the stakes of the shame of the masturbation act to the shame (and, actually, crime) of what he was watching. And it that moment, for a techie like me, my suspension of disbelief went out the window. The important question remains unanswered, which is: how did they show what he was watching? You could say that, as an spectator I was one of those rare skeptic neighbour who needed stronger proof to believe he actually did that. It is shown as a very dramatic situation but that could actually just had been overreaction of a teenager and his mother.
At the end, for better or worse, it doesn't matter if you did it. It matters if they can reasonably prove it.
DISCLAIMER: Of course it matters if someone is a pedophile,
pedophilia indulging that disorder (in the form of watching such content and supporting that industry) is a heinous act which I do not condone nor tolerate. I'm talking about the stakes and rules that the episode presents, because the episode could work pretty much the same with any other apparently-shameful-activity-that-turns-out-it-was-actually-something-despicable-and-illegal.