With fossils, as with living animals, any time you see pentaradial symmetry (five sides, or five radiating arms), think Echinoderm. In this case, as Gary said, it's the mould of an isolated plate from an echinoid test (sea urchin shell). The concentric circles in the middle were part of a 'tubercle'; the ball-joints onto which the urchin's spines attached. In this instance it's quite a large tubercle, which points to an order of large-spined echinoids called the Cidaroidia.
Worth noting that your fossil didn't originate at Pett Level, where the fossil strata there were formed in a freshwater esturine/lagoon area. Instead, like all the flint pebbles along that beach, it has been shifted by wave action along the coast from where it eroded out of the the chalk cliffs, thousands of years ago.
Thank you! That's really interesting.