I believe the answer is technically no to using your own sun glasses. Some companies have sunglasses that they issue out and they’ll issue sunglasses clips that can attach on to those who wear glasses. Having said that, it’s not something that in my experience is enforced and plenty of people have their own sunglasses just like plenty of people have their own safety boots/shoes (or trainers!).
It is indeed, even for non prescription glasses. This was rigorously enforced at my old TOC, who insisted on issuing utterly useless, cheap and nasty sunglasses that broke at the drop of a hat, on the basis that some non railway types might make it difficult to distinguish between signal aspects.
I always suspected it was nonsense, and I’ve so far managed four years and counting without spadding at my current TOC, while wearing my trusty Wayfarers!
It’s much more important to be sure when it comes to prescription sunglasses, of course.