A Traffic Regulation Order has to be made, in accordance with the Road Traffic Regulation Act 1984.
Before this happens there is consultations between the local council, police and sometimes other emergency services if parked cars are causing problems for fire engines or ambulances getting to emergencies.
Then there is public notices in the local newspaper and displayed on site, usually on lamp posts adjacent to the area.
Members of the public can object. If these objections cannot be resolved then it is passed to the Highways & Transportation Board who make the final decision.
The whole process can easily take a year or more. I live not far from a very large hospital and nearby residents have been petitioning the council for nearly 5 years for double yellow lines because of the high number of hospital staff and visitors that park in their cul de sacs all day causing access problems. The matter is still not resolved.