River, forming part of the border between Scotland and England, that enters the North Sea at Berwick (5)

I believe the answer is:

tweed

(Other definitions for tweed that I've seen before include "Woollen material" , "Thick woollen cloth - northern river" , "Fabric; river" , "Woollen cloth - Scotland/England border river" , "Scottish and English river" .)

I've seen this clue in The Independent.

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