Good question Andrew, I am probably wrong, but all my heavy barrels do not have HV near the rearsight.
As the H barrels were produced from 1933 on, the same time as the Mk.7 round was allowed to be used by the Rifle Club movement, I just made the assumption.
The Mk.6 rounds were used up by 1934, the HV round effectively introduced at the same time as the H rifles in 1933.
1930 saw trials with the modified LE barrel, 1932 saw the production of the first dedicated H barrel and it's subsequent issue to Rifle Clubs thru 1932-34.
The H rifle was for sale at four pounds, a barrel without sights one pound sixteen shillings.

Just noticed that I have one heavy barrel with SC/HV on it, but it is a shortened LE barrel.