I have come across the sponsors mark A.G.R. before.... The AGR initials, with dots in between as this "A·G·R", are for Arthur George Rendell of 40/42 Clerkenwell Road, London who are recorded as importers of Swiss watches from 1907
I took this info from here: Vintage Watch Straps - Case Marks
As you can see, the one on this site is also referenced to Edinburgh - not London....