Is the .303 round you are using to check the chamber a brand-new factory one, or a reloaded one? If it is a reload from another rifle, and only neck-sized, it might not fit in this rifle even if it is a .303!

Could it be chambered in one of the 303 wildcats like 303/25 or 303/270? These would also not chamber a standard 303 round.

If your rifle is a .308, about the only Ishapore 2A 7.62 part which would be of any use to you is the magazine.

Although intended for a No 1 style action, they will fit the No 4 or No 5 action and feed reliably - better than the Sterling 7.62 mags in my experience.