The story
The term "B road", or "B-Road", in British road classification refers to secondary roads, typically narrower and less important than A-roads (primary roads) but more significant than minor roads (C-roads or unclassified roads). Prefix "B-" [which likely stands for "British" or "Branch" in the context of roads. These roads were originally classified as secondary roads in the UK road network] + "Road".
Etymology from Wiktionary, CC BY-SA 4.0.