Hi Grouch,
There are a few characteristics of the nomenclature that make it clear to me when this pipe was likely made. The REG's number refers to a REGISTERED DESIGN. Barling would protect its designs, in this case the stem design, from being stolen by others by registering the design. For all intents and purposes this functions like a patent.
In the US it was 98046. One might have expected the UK REG number for this since the four digit model number indicates that the pipes was sold in the British Commonwealth. Pipes made for the US market had a different model numbering system. But as the UK RED'd number had expired in 1944, that leaves the US number.
Then there's the font used in making up the "BARLING"S MAKE" logo. The stamps used changed, with some overlap, throughout the 20th century. Once you can recognize the relationship of a particular logo stamp to a place in time, that's another clue. Your's is a '40's to early '50's logo stamp.
Prior to WW2, Barling rarely stamped either a model number, or TVF (The Very Finest) on any of their pipes. After the War it became common for them to do so.
Ye Olde Wood started out as a grading and was applied to pipes made with wood of a finer figure than average. It also became synonymous with their red stain, but the two are really not related. You will see the YOW stamp on pipes with different colored stain or natural finish. It did remain a step up from their base grading, a nicety that is lost on todays collectors.
MADE IN ENGLAND. is a standard COM stamp for Barling, before and after the War. Sometimes it appears with the period, sometimes without. There's no significance to that.
You didn't mention a size stamp, which would have appeared to the right of the COM stamp, which for this pipe I think would have been EXEL, which stands for Extra Large. There is no significance to the lack of a size stamp in this instance. Barling was consistently inconsistent with their stampings.
Because of the time frame in which this pipe was made, the briar is Algerian.
Your pipe appears to have been very lightly smoked, based on the crispness of the rim and moderate carbon buildup. A little spit with a rag should take that off.