Designer intent is that you can end concentration during another's turn
It is not clear to me what the purpose of the clause "at any time (no action required)" would be, if you could not do it on any turn. If the intention would have been to only be able to do it on your turn, this would be an extremely counterintuitive and misleading way to express that. You then should say "at any time during your turn (no action required)", or require an action so the caster can use the Ready action to do it on another's turn.
There is no official Sage Advice Compendium ruling on the matter, but this interpretationis alsois supported by a statement by Jeremy Crawford on twitter:
You can, indeed, end your concentration at any time, not just during your turn. #DnD [emphasis added]
This is separate from another time where he just quoted back the rules text. Now, Crawford is not an official rules authority any more when he speaks on twitter, and he has been known to be inconsistent or self-contradictory, but he is not here, and he still is the lead designer of these rules. At least in regards to intent of how the rule is supposed to work, you can also do it on anothers turn.
This of course still leaves it up to the DM, in the end.