I think so but I am wondering if it is the 'lesser stick' one. It is attached at one end with the frilly bad look that the feeding end has. I have no experience of 'lesser stick' case moth so don't know how they appear.
Did you inadvertently have an unseen lodger Alison? I agree with Wendy that the moth is Uraba lugens and to the best of all out combined knowledge, the case is a Psychidae.