Here's how it looks to me, at a glance: It was never a service rifle; no Gov't stamps. It was made as a commercial rifle by BSA, almost certainly of the MLE ("Long Lee") configuration, and probably used as a target rifle. The barrel was cut down to its current length in order to compete in matches with the SMLE. The muzzle looks like a Rifle Club conversion (i.e., a Lithgow Heavy). The only odd thing is the advertised barrel length of 26-1/4", because the standard rifle club length was 25.2". Maybe they're measuring it incorrectly.

The buttstock and forend are not in any of the usual Lee Speed styles; they look completely custom. I'd bet that forend and that barrel did not originally go together, as witnessed by the extra space on either side of the barrel. It also looks like there was a rear sight on the barrel that was removed.

I think there was a lot of custom work on this gun. It doesn't look like an original sporter, but it certainly is a commercial gun, and it looks beautiful. Maybe the lucky owner will chime in and confirm the barrel measurements.