Sussex town luminary eats sandwiches (3)

I believe the answer is:

rye

'sussex town' is the definition.
(town in East Sussex)

'luminary eats sandwiches' is the wordplay.
'sandwiches' indicates a hidden word (the answer is sandwiched in by the clue).
'RYE' can be found hidden inside 'luminary eats'.

(Other definitions for rye that I've seen before include "Cereal grain" , "Grass - whiskey" , "Cereal grass - Sussex Cinque Port" , "Bitterly regret" , "A Cinque Port; a grain" .)

I've seen this clue in The Telegraph.

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