It depends on what you mean by "traffic tickets". In the United Kingdom, there are civilian traffic wardens who can issue tickets for car parking offences. I am not aware of them being able to issue tickets for any other types of offences. I understand that speed camera tickets may be issued by a private company. But in both these cases, the tickets are being issued on behalf of the police forces.
In the United Kingdom, the local authority (local government) is responsible for its local police force and this money goes into local government funds.