I think badge numbers started at 1001 (I've never heard of or seen one lower) and were issued following the 1931 transport act, so that badge must have been a very early issue, almost certainly in the first few days of the legislation. Your father may not have been the first to have it though, there were re-issues of returned badges (known to the drivers as "dead men's badges") where a badge was returned to the traffic commissioner if a driver retired from driving or moved to another traffic area, (as he would have been issued with that area's badge at his next licence renewal).
Hi Lloyd
Going back to the 1950s, I can't remember ever seeing a 3 digit badge either, although plenty of 4 digit ones, both for drivers and conductors.
How long did their licences last, as I can well remember one outer circle conductor who I knew for several years, and he had a BB badge for all that time.
Kind regards
Dave