Great advice tanith and thatbags, thank you, I shall follow those up. Yes, they are definitely silverfish, eating from the edges inwards, not moths or carpet beetles. granjura I don't think moths would stick to the edges the way these do!
According to Wikipedia, silverfish predators are earwigs, house centipedes, and spiders. I am sending DH out to hunt for earwigs and spiders tomorrow (I don't fancy the centipedes much). He is supposed to be the hunter gatherer of the species, isn't he? I could make him a little net.
Alternatively, deedaa, flowers and roses (what a lovely bouquet) since you like them, please feel free to come and round mine up and take them home with you. The carpet is a good wool one, and it is looking very scraggly at the edges where they have been.
Wikipedia info here