It is definitely a moth. But I'm struggling with the name Malthius creticus. Fauna Europaea online doesn't even have the genus Malthius (http://www.faunaeur.org/).
I'll have a look at some other sources, but can't promise quite when, sorry (dealing with storm damage here in Cyprus at the moment).
Adela paludicolella, one of the fairy longhorn moths - see
As well as the prominent white band, note the small white mark nearer the wing tip, and the small white marks on the outer joints of the legs.
From the relative shortness of the antennae, I think it is female.
(Adela australis is similar, but I don't think it has been recorded from Greece/Crete.)
I think I must have had a brainstorm, not realising that it was a moth. (I've been looking at so many pictures of beetles over the past month that I've got beetles on the brain). I have about 50 moth species on file from 8 families but the Adelidae is a new family for me. Thanks again for the very helpful positive ID.