As Barry indicates, parking on double yellow lines used to be a criminal offence, with enforcement being the job of the police and traffic wardens. Fines were paid into the court system.
In many areas that is still the case. (The only difference is that traffic wardens have usually been replaced by designated PCSOs).
In other areas, the local authority has applied to the Secretary of State to take over control of parking enforcement. (Such applications have been possible since the 1991 Road Traffic Act introduced 'Decriminalised Parking Enforcement'. That Act has now been replaced by the 2004 Traffic Management Act, and the matter is now called 'Civil Parking Enforcement' (CPE)).
Where CPE is in operation, it's not a criminal offence (per se) to park on double yellow lines, and the police will ignore transgressions. If a 'contravention' (rather than an 'offence' as it used to be) is noted by a 'Civil Enforcement Officer' ( = council parking warden), a civil debt is created, which must be paid to the local council.
Here in Suffolk, the police force have designated PCSOs (with a 'Traffic' flash on their shoulders) whose prime duty is to look after parking enforcement in areas like Stowmarket (where CPE is not in operation). Just down the road in Ipswich though, neither those PCSOs nor any police officers have the power to 'ticket' a vehicle solely because it's parked on double yellow lines. (Of course, 'causing an obstruction' remains a criminal offence, irrespective of the presence - or otherwise - of double yellow lines, and can always be dealt with by police officers).
Chris