I have owned 3 Biagio Cues. My first one was clearly a much higher quality than the the others. Featured Brazilian Rosewood forearm, butt sleeve with 3/8 x10 pin,SS half joint with woven phenolic collars and rings. Also it had a killer super tight grain shaft with old Micarta ferrule. From the build, I believe this cue was made in England BCE ? by real craftsmen in the late 70's early 80's.
The other 2 I have owned were veneered 4 pointers with 5/16x18 pins and were nice but not the same overall quality as the big pin model. I believe they were later production models ( late 80's early 90's) were made in Taiwan and looked much like the one on eBay you posted even though it has a 'Made in England' sticker on it. It might have been 'finished up' in England with Taiwan blanks, joints etc.
Just my take,
-Kat,