At low tide, the area below the car park, almost underneath the inner arm at the Old Fort on Shoreham Beach used to be good when I was a kid. Don't know what it's like now though as there have been a few changes in the last 30 years or so.
When, as a kid, I used to drop my line along the inside wall of the west arm of Shoreham Harbour, in the forlorn hope of catching some proper fish - which you could often see in the water when it was calm - I always used to end up reeling in crabs. Bloody nuisance they were.