SMLE Barrel inspection stamps

[muffett.2008]

If you have a heavy barrel, then it is definately a Lithgow, these barrels were not produced by any other country.
Heavy barrels were produced from 1932 on, specifically for the Rifle Club Movement, but also were used in the H rifles and were fitted to Service rifles in the last years of the war, the markings on a H barrel will have a large H on the nocks, you may have the letters AJ, AV or VS in close proximetry to the stars.

You have not said if the stars match what I have pictured or if they are the rust * astericks.