Aloka and Terre à Terre are pretty near Palace pier. Other than that last time I checked (last year) the chips from the stall by the crazy golf, near to Palace pier (on the left of the pier if you're looking out to sea) were vegan but do check again as their cooking methods may have changed. Same goes for the chip shop on the seafront on the corner of Ship Street, a bit further towards West Pier.
Yesterday I couldn't recall the name of the pub the chef from the Earth & Stars had gone to (I now know it's The Royal Sovereign on Preston Street) but thought I'd found it when by chance I saw a sign outside The Bedford Tavern on Western Street offering vegan Sunday lunches. However on enquiring inside it seems they had just parted company with the chef who did a vegan option so they aren't offering vegan food at the moment after all. I'll have to try The Royal Sovereign another time.