Hi there, not trying to be rude off the bat, but Lock Stock and Barrel Investments moves more guns in a year than many on this forum will possibly ever see in their lives, do you really think they can't differentiate between bluing and parkerization?
Older parked guns will generally (in my experience) just turn a very flat matte grey or black depending on what original mixture they were finished with. The way this gun is turning a rich plum would certainly indicate an older re-blue, potentially in the late 40's or early 50's before the glitzy high-gloss bluing became all the rage for both factory and "restored" finishes. The scratches on picture 5 of the ad appear to be below the surface of the finish, and the "Webley" and Crown/BP on the left side of the frame in pictures 6, 8 & 9 all appear to have been partially obliterated when the gun was being polished before refinishing.
To answer in short, no this gun does not appear to be parkerized or to be presently wearing a factory finish. If you would like to see some examples though, I can try and dig out my Enfield No.2 Mk1** revolver finished with Suncorite and a couple older blued Webleys for comparison sometime