Well, It sounds like the simplified version of the MkIII that was made during World War one to ease production. It could even be that it may be a none-UK version as the No.3 was the standard Lee-Enfield throughout the empire, even during World War two.
It may well be the reason the aforementioned states did not adopt the No.4, maybe multiple rifling is too confusing for the colonials.
mdn it could be 2 groove savage rifling badly worn, nothing surprising there! Is the rifle stamped US property or have a S in a square? If the bolt removal groove is in the area of the bolt its one of the simplified for production models from savage made under lend lease! bring it along!
No4s were made with 2,4,5 and 6 groove barrels, and 3-groovers were tested but not produced. I don't think that there has ever been a one-groove barrel on an Enfield, or any other rifle for that matter - surely such rifling would leave the bullet asymetric and therefore very unstable?
The only other thing I can think of is that someone has got hold of a part-cut 2-groove barrel and fitted it to the rifle. Evenso, I can't believe that it would shoot straight, for the above reason!
Whereabouts are you? Your rifle sounds interesting, and a quick look at it might let us ID it.
BTW, I'm an Enfield collector/RFD and I own, or have examined, 100s and 100s of the things.