That's odd. Does the bore look central? Does the thread look ok? What caliber is it?
BSA sell a good mod (the VC) that is adjustable for each caliber, but I wouldn't say to go out and get a new mod until you figure out what the problem is.
My old Ultra always shot beautifully with the mod on. Never fired it much without the mod as it was so loud...
This is a bit left of field but it could conceivably have something to do with barrel harmonics...possibly try putting the mod on, and then adding a weight at different parts of the mod and barrel, to see if it affects grouping.
How do you know there's no clipping btw?