After an unsuccessful application for a permanent academic position in the UK, should I call and ask details about the selection procedure?
You can call and ask, but you are unlikely to get anything useful. You will most likely hear that your CV was very good, but that there were stronger applicants. If the head of the search is really good, they might actually look at your CV again and pick a weaker aspect of it (no matter how strong a applicant is, there is always a weaker aspect of the CV).

If you want to know about your relative qualifications, ask whoever is writing your references. If they do not know about the UK system, find a colleague that does and ask them.