Which roads do you mean? I think that in most cases where the pavement has been partially designated for car parking the council tends to drop the kerb anyway. If it's not been dropped it may be that parking isn't allowed.
I'm referring to the ladder roads between Grierson Road and Stondon Park (Riseldine, Tatnell, Parbury, etc).
Parking is definitely, officially supposed to be part on, part off the kerb at the direction of the road signs and markings. I've no idea how long this has been in place but the kerbs were definitely not dropped when it was implemented and on some of the roads it's like parking on the edge of the white cliffs of Dover.