If the 7.62/308W round fits, and the .303 doesn't, then it is a fair bet that the rifle is in 7.62 calibre. A chamber cast needed, maybe?
Can you give a photo of the bolt head, showing the shape of the extractor claw? A proper conversion would have a different extractor shape.
If the conversion was done in the UK, then it SHOULD have been re-proofed and wear markings to indicate this - for example small printing stamps saying 7.62 x 51mm, most likely on the bottom of the exposed portion of the muzzle near the foresight.
If it was done in Canada, or the US, or Australia
these markings would not been seen.