Unified threads didn't exist until about 1948. They were based on American threads, which is why so many of them are effectively identical, although some of the clearances are not identical. They have the disadvantage that unlike BA, and to some extent BSW and BSF, they are weaker, being 60 degree thread angle rather than than the 55 degrees of BSW and BSF and 47..5 degree angle of BA - which is in any case a metric thread. Plus it's the only logical thread series where each step down in is 0.8 of the pithch above e.g, 0BA is !mm pitch, 1 BA is 0.8mm, etc...It is actually the Swiss horological Thrury thread, which went down to number 27..... and was down to the tensile strength limit of high tensile steel screws available....
BA screw threads as such were adopted at Montreal conference in the late 1800s, although the first imperial standards for them appeared the early 1950.s. Prior to this , they were all speciified in metric terrms... Why change/ one can only assume because the title was 'British'......