This post is from last week, but the issue is lingering on, and imo some rather important things haven't been mentioned so far, so I guess it's fine to respond. I'll try to explain what I believe to be historical reasons for a general alertness over this specific type of pronunciation. My opinion on the Corbyn "incident" at the end.
First of all, I don't think @Classical Mechanic has been correct in his interpretation here. I don't think that associating Epsteins Jewishness with his crimes was intended, or even an unconscious subtext. Just my gut feeling based on the video snippet, but I'm rather sure about it.
I also think @Zlatattack is wrong in assuming the point of contention is a perceived "disrespectful" mispronunciation of a name of foreign origin (and a case of some Jews demanding privileged treatment over other minorities).
It's not too easy to think of an apt analogy for clarity, but a rough equivalent might be a white person inappropriately calling a black man "boy". If you're aware of the history of that word in the context of black history, you just don't do that. Even if it's just a glitch, some people will be on alert and pay close attention to what that person's up to. And they're right, even if the questions of severity and motive still remain to be answered, and may lead to a .
When done publicly, such a wording will likely draw criticism, especially when coming from someone who's already in hot water over related issues. This will in turn trigger responses saying it's absolutely nothing, and complainers should stop being so damn touchy. You'll know the inevitable backwash of ignorance and hostility that will go along with it. But informed people will be aware that a whole history of stereotypization and persecution can very well be evoked by an innocent-looking three letter word, depending on context. When used in a specific way, it symbolically sets black people back to being subordinate to white people, targeting the liberation they have gained since then.
It's basically the same with the "re-Judaization" of assimilated Jewish names. This has been a tool of antisemitic othering for a very long time. Antisemites used and still use it to mark the targeted person's supposedly alien nature, and to uncover the "hidden Jew" behind a seemingly assimilated citizen. The underlying logic behind antisemites exposing a Jew's "real name" is to make the whole history of Jewish assimilation and emanicipation null and void. And everyone with a grasp of Jewish history knows what that means.
A recent example would be Trump demonstratively calling Jon Stewart "Jonathan Leibowitz". (Stewart's response.) Now, I'm sure Corbyn didn't do something like this there. It's one of those things where purpose makes the difference. In general, I think critics accusing him of that kind of antisemitism are on the wrong track.
So what do I make of it? While there has certainly been justified criticism of Corbyn, this case rather looks like an unfortunate blunder to me. It surely warrants a critical mention/correction, because, as I said, if you're conscious about these things you just don't do that. And the context I tried to give above is why reflexive dismissals of such complaints are ignorant - at best. But I also see it as a minor issue, and not a case of dog-whistling, which is why I think scandalizing it wasn't the way to go. Especially in the toxic British media landscape. But my guess is that this particular episode will have resonated much less with British Jews than other ones. They're not a uniform "community" anyway, and the whole range of opinions will exist about it, in whatever proportions.