Hiya, thanks for trying to improve the one-way system in Lancaster, but I think motor_vehicle=permit is the most appropriate tagging, according to the wiki (https://wiki.openstreetmap.org/wiki/Key:access#List_of_possible_values).

motor_vehicle=no means access by motor vehicles is physically impossible (e.g. due to the road being too narrow) or completely illegal (e.g. no entry signs).

motor_vehicle=destination means that any vehicle is allowed as long as it’s going to a destination on that road. Typically this is signed in the UK as “except for access”.

The signage here says “authorised vehicles only”, which implies motor_vehicle=permit to me.