Yeah, Cornwall was most famous for its tin, but there was a reasonable amount of copper too - particularly in the Carnon and Tamar valleys.
There were also very productive copper mines around Great Orme in North Wales, which would have only been a couple of days' travel by boat and were frequently visited as part of the same Atlantic Bronze Age trade routes as Cornish tin.
There were some exceptions on the British Isles. Even some mines that had both.