The connection between this word and Old Welsh circhl (from Proto-Brythonic *kɨrxl, from Latin circulus) is unclear; perhaps there was metathesis of the r and l to *kɨlxr followed by cluster simplification to *kɨlx. The fact that both Breton and Welsh show reflexes of *kɨlx means that such a change must have happened before Proto-Brythonic broke up into its daughter languages, in which case Old Welsh circhl would reflect either an unaltered byform existing alongside the altered form or a reborrowing from the Latin.
A possibility mentioned by Morris Jones is that *kɨlx is inherited from Proto-Indo-European *kuklós (with metathesis of kl to lk > lx) and thus cognate with Ancient Greek κύκλος (kúklos), Old English hwēol and Sanskrit चक्र (cakra).
A third possibility is that *kɨlx could be borrowed (still with metathesis) from Latin cyclus, from Ancient Greek κύκλος (kúklos).
*kɨlx m