I have not had that problem . I am thinking possibility of getting oils from your hands on the structural bar. I would try cleaning the bar and inside of clamp. If that fails, I would lightly sandpaper the inside of the plastic tube.
Usually the threads on the ends of the bolts are peened after the nuts are installed. Were you able to remove the nuts without ruining the threads ? Then , after reassembly , how did you keep the nuts from coming off?
Cool add to the fleet. Back in the 50s' I rode one too. We called them English Racers. Today would be Distinguished Gentleman's Ride . Doubt that you would find any Tweed Rides in the New Abnormal ! If there is a date stamped on the rear hub shell, it could also date the bike.
When in doubt- leave it out ! Good discussion though. A local beach town here does want to be active in fighting bike theft . I like the ideas mentioned about putting your info inside the frame. So does this Police Department : https://asburyparknj.seamlessdocs.com/f/BICYCLEREGISTRATION
Interesting tip. A long time ago I was told that if you first applied cold cream to your hands, before work, it would fill the pores of your skin. That would keep the grease and grime on the surface, making it easy to clean.