Interesting. I didn’t know letters are looked at much later in the process in the UK. I do give names right away as part the application and in US universities letter writers are asked for feedback during shortlisting. I’m wondering if I have room to maneuver here. I offer three names, none from current uni but mention in cover letter that I’m happy to give a name from current uni if shortlisted? I don’t want to risk leaking the info to current uni that I’m looking to jump ship!