I remember now that a small brewery was once in The Egremont, down the side road (York Place) at the back, and/or opposite?
Edit. I moved to Worthing about 30 years ago, and I did a lot of work for that pub and The Royal Oak, opposite. That's when I was told of the brewery of the old days.
That signage was only brought back to life recently when it was totally refurbished, to a great standard imo.
It's possible that vegster or Questions could confirm or tell us more.