Kevin: I have seen a couple of the 303s sporterized by Parker/Hale and thought they were pretty good looking and very handy. One in particular seemed to have a thick, almost even a bull barrel, but it was a #4 MkI that had a thicker barrel than the earlier model (No I, Mk3). None the less, it looked good and felt good when brought to the shoulder. The action was nice and smooth, too.
As I understand it, there were a couple of firms in England that took the SMLEs and sporterized them for the civilian market and possibly even some American sporting firms.
Unfortunately, some youngster with little appreciation for older rifles wound up with it before I could stake a claim to it. Bummer.
I guess I should have laid my money down first. Mikey.