It's possible that it was built by W & S, but I kinda doubt it. I think it more likely that it was built by Westley. Look the barrels over for a number that does not match Westley's. The trade maker's number was typically put somewhere in the vicinity of the fore-end loop. Late pre-war double rifles that Webley built for the trade had the 5-digit number on the left side of the fore-end loop, close up against the barrels. If there's a non-matching number there, that's almost certainly the trade maker's number meaning that it was made for Westley by someone else.
The "White Hunter" models were generally basic DRs intended for hard service. I'm not sure, but it's my understanding that the "Gold Name" label is a generic used by the trade, not Westley.
For DR work I use J. J. Perodeau in Enid, Oklahoma. J. J. came up through the Liege trade and was with Marcel Thys before coming to the US. I've used him for a number of DR issues, and his work is superb.