At the time the referendum was taken the legislation stated quite clearly that is was advisory. That cannot be disputed. It is a fact.

The government believed it had the authority to be bound by the result of that referendum, and their belief was never questioned by Parliament.
The electorate were told the result would be binding, and were given no guidance by any political party or campaign group that it was not.

and on the other a BBC report of what the government legal advisor said during an interview, I am more inclined to regard the former as more reliable.

Read it again. It is not from an interview it is the government's case as put to the High Court.

BWM,
but the High Court says (correctly) that parliament is sovereign,

Clever of you again to know they were correct when the appeal has yet to be heard!

The government wish to trigger Art. 50 by Royal Prerogative,

Yes. That is how they intended to make the referendum binding despite the legislation you keep on about.