Council Fine CheckCouncil PCNs go to the registered keeper shown by the DVLA. For hire and lease cars that is usually the hire or leasing company, so what happens next depends on the type of agreement.
Short-term hire
A vehicle-hire firm can make representations on a specific ground: the vehicle was on hire under a hiring agreement and the hirer signed a statement of liability for PCNs during the hire. It must give the hirer's name and address (SI 2022/576, reg 5(4)(d) and (7)). For London moving traffic PCNs, London Tribunals says the hire agreement must be for under 6 months and the firm should supply a copy (source).
The council then deals with you as the hirer. Watch for a new notice in your name and use your own grounds; the deadlines run from that notice.
Admin fees
Hire firms may charge an admin fee under the hire contract for passing on your details. That is a contract matter between you and the firm, separate from the PCN.
Lease and company cars
If the leasing company is the registered keeper it may pass the PCN to you under the lease terms; check your contract. If you are the registered keeper of a leased or financed car, the PCN is yours, as with any car you own.
"I was not driving"
Council PCNs are owner liability: not being the driver is not a ground by itself. The grounds are about ownership, consent and the contravention, not who was behind the wheel.