The Holdsworth post war years were full of ups and downs. The immediate years, from 1946-50 saw, the production of only three models. The Cyclone-de-Luxe, topped the range, identified by its Gothic spear-head lugs, with added elongated spear, along the top and down tube, at the head tube and, the top tube at the seat cluster. It was available as a Road frame or a Track model, at a price of £15.15.0 in 1949. The Cyclone model came next using the same lugs but without the addition of the elongated spear. At £13.10.0 it soon became the most popular model, outselling the De-Luxe and, the third model, the La Quelda, a lugless frame, introduced to answer the increasing demand for a welded frame.
W F Holdsworth
...from the brief description, it sounds like maybe a track bike. But sans pictures it's hard to tell very much.