Think it goes beyond the BBC as I've not seen exit polls mentioned elsewhere in traditional UK media or indeed on UK based social media.
Yes, it is beyond the BBC - it's in Ofcom rules. I was pretty certain it was based on UK law, but I can't find it anywhere in the most relevant Acts, so perhaps I'm wrong.
It's interesting to see what newspaper websites are doing: many reporting no polls; the Express and Daily Mail reporting freely; the Independent initially reporting with a lot of detail, and then taking down all of those stories (was there an 'intervention'?)
The BBC is somewhere in the middle, reporting which parties are "celebrating" after the publication of exit polls, but with the caveat that they are barred from publishing the poll results themselves.
This all feels like an antiquated curiosity when we all have such routine access to foreign media. It's fascinating in its own small way!