This individual 12mm long, another was 22mm long. The longer one was observed on a rendered wall ca. four days ago. Both are on a concrete pavement adjacent to that wall.
Yes there are really interesting. I have often wondered what they are. I have also wonder if they could even be from another group - e.g. terrestrial caddisfly larva?? I don't think we can assume they are Psychidae = case moths. As DonHE would say - should raise them to find out.
Interesting! Are there such things as terrestial caddisfly larvae? I understood they were all aquatic. Similar creatures are illustrated here https://www.flickr.com/photos/dhobern/albums/72157609580850398/ in addition to the other link I sent. Update: You suggest caddisfly larvae, but have listed them as "Lepidoptera immature". The terrestrial caddisfly larvae which I can find is a reference to a single species from the Family Calocidae, Caloca seneva, restricted to Tasmania and found in damp environments.
Thanks, MichaelBedingfield, that's an interesting idea to explore. I can only find information about lacewing larvae carrying bits of debris from their prey. These things are most definitely wholly encased with sand grains, not merely carrying something. Your proposition seems to suppose a new phenomenon. Further individuals have been seen suggesting this is not a coincidental behaviour of the two individuals reported. The weight of evidence continues to point to something other than a lacewing.
Another group of case bearing inverts are the case bearing leaf beetles - Subfamily Cryptocephalinae. I am not suggesting your critters are these are they have smooth cases. As Neuroptera tend to be predators the larvae tend to have large intimidating pincers.