I took my test in an A35 which had a starnge sort of system, could not really be called independant.
The rear brakes were rod operated and were effectively the handbrake, there was a slave cylinder actuator under the handbrake lever which would apply the handbrake (rear brakes) when the hydraulic foot brake was operated, it had a sliding linkage so that the handbrake lever would not come up when the footbrake was applied.
At least that was the design but they hadn't reckoned on the apprentice Chancer bolting it up solid to get a more solid pedal, each time the footbrake was applied the handbrake would come up and lock itself on by the ratchet and I then had to release it.
Believe it or not I took my drivin test in that death trap in that condition 2 weeks after my 17th birthday and never having had a single lesson, and I passed
Tha handbrake was on the right by the drivers door and I thought hidden from the examiner although I'm sure he was aware of exactly what was going on, he was either impressed with my right hand dancing around releasing the brakes and my other arm and clutch foot having to double de-clutch in every gear or he felt sorry for me.
I think, dependant on the age of the vehicle that a hydraulic handbrake is not road legal as a service brake but if the umbrella one is stlll there whats the problem?
Most modern vehicles with these infernal automatic parking brakes are they not hydraulic? I have only ever driven one modern car with one and dont wish to repeat the performance I was trying to drive it out from being bogged down in a sloping field for the owner, something I am usually very good at and the handbrake thing was working against me, ditto when the tractor was towing it out.