See
THIS LINK
Has the council fulfilled its obligations under Section 5
Section 13 is also interesting, particularly the reference to
a local authority should appraise its parking policies and the way those policies are being implemented, to see which traffic management objectives are being met and where improvements are needed what have height restrictions have to do with traffic management
Also of note is the definition
A Controlled Parking Zone (CPZ) is a parking scheme which provides parking controls to ensure a balance of the needs of residents, businesses and visitors whilst ensuring the management of congestion,
again it's all about traffic management, nowhere can I find any reference to restricting access to parking on the basis of vehicle height.