Loads of scientists are popular science writers and even the almighty Hillside advocates them.
But you've left off the bit about him being an Astrophysicist and a visiting fellow at the University of Sussex.
I didn't say he wasn't a scientist - I said he wasn't a scientific researcher. Two different things - a scientist is trained in science. A researcher uses that training to generate new knowledge and ideas. As far as I'm aware Gribbin doesn't do that, although he is good at taking the ideas of researchers and writing them in a manner that is understandable by the public.
So in that context Gribbin isn't like either Hawking or even Cox who are (or were) both researchers as well are great exponents for public understanding of science.
As far as I can see Gribbin hasn't been actually involved in any research since he completed his PhD (which is itself considered training to be a researcher) over 50 years ago.
I cannot find details of him being a visiting fellow of Univ Sussex but this was where he did his degree back in the late 60s and being a visiting fellow doesn't imply any involvement in research - it may be for profile and for his public engagement activities.