I can confirm that R.E.W. Reynolds frames were made by Woodrup in Leeds and painted at Ellis Briggs in Shipley, West Yorkshire (a separate town but in the same metropolitan area of Leeds and Bradford). Well at least some of them were in 1975 when I was learning to build frames at Ellis-Briggs. Rod and Bill were the painters and their room on the 2nd floor was also where the frameshop was located. If I remember right Jack Briggs told me that they helped Woodrup get started in the 50's after some kind of falling out with Bob Jackson. I spent a day at Woodrup while Steve showed me how to do a Masi style of scalloped style seat stay top treatment.
It is highly probably that E-B painted your white and flam red frame. One time I remember taking some frames to the chroming shop located in another small town about 15 miles away. One trick E-B liked to do was chrome the center of a seat tube before building it into a frame. Then the 2nd color bands were chrome.
Here is an example of a "it is a small world" moments". While I was there, Rod and Bill painted a Woodrup in an unusually complicated maroon and yellow and other colors. I would watch the progress because Andrew (the young frame builder then and now passed) and I would eat lunch in the paint room. While I didn't try my hand at painting in England I did learn the techniques of how to do the complicated stuff there. Anyway when I get back to Ohio in the fall to continue teaching high school, I go into the local Kettering Bike Shop and to my total amazement, there is that same Woodrup frame waiting for its owner to come pick it up. What are the odds?