Shock waves produced by magnetic compression are called transverse when the magnetic field contains no component in the direction of the shock wave normal. It is experimentally well known that very strong shocks of this type show classical MHD behaviour in terms of both jump conditions and structure. It is also known that relatively slow transverse shocks can be of an ionizing gasdynamic type with no jump in the imbedded transverse field. Since there are fundamental differences in both the structure and the jump relationships of these two types of shock waves, it is of interest to investigate the transition behaviour in the intermediate shock speed regime. A previously widely accepted model due to Kulikovskii & Lyubimov and Chu assumes no precursor ionization and requires significantly large values of the magnetic Prandtl number, Pm, within the shock structure. That model is shown to be physically inappropriate because experimentally observed transition speeds and corresponding post-shock temperatures imply negligibly small shock Pm values. Also in that model, MHD conditions are approached only asymptotically at large shock speeds. The present precursor ionization model assumes effectively zero Pm values throughout transition and into the low-speed MHD regime. As distinct from the previous theory, this model predicts the attainment of full MHD conditions at and above a well-defined finite shock speed. The assumption of a characteristic post-shock temperature model for the ionization mechanism allows unique jump relations to be formulated independently of other transport mechanisms. Results include computed values of various jump ratios and the electric field as functions of shock speed throughout gasdynamic, transition, and MHD regimes. The solutions form a one-parameter family depending on the relative combination of upstream magnetic field and density (e.g. the Alfvén velocity). Shock structure phase plane trajectories are computed at a number of typical shock speeds throughout transition.