The answer to your question really depends upon the date that the charge was issued to your vehicle.
If the parking event occurred before 1st October, then under the terms of the law of contract, the liability for the charge rests with the driver of the vehicle, and the keeper of the vehicle has no liability to pay the charge. Whilst we suggest that it is good practice for the keeper to disclose the details of the driver of the vehicle, they are under no legal obligation to do so.
However on 1st October this changed with the introduction of the Protection of Freedoms Act. Whilst the act itself deals with the banning of the clamping and removal of vehicles where there is no lawful authority, the Schedule 4 of the act enables the parking operator to pursue the keeper of the vehicle if no serviceable address for the driver is provided. Unfortunately a ‘serviceable address’ means that the details must fall within the jurisdiction of the legislation, that is to say the address must be British. This is actually a better process than if a ticket is issued on the public highway, where the keeper is automatically liable, with no opportunity for driver disclosure.
If the charge was applied to your vehicle after 1st October, you could send the operator the details of the driver if you wish, and the operator may try to pursue the driver. However it may be that the operator will then revert to you as the keeper of the vehicle to obtain the outstanding charge, as he is allowed to do so by law.
In this respect, I would suggest that it would be down to you to obtain the charge from the driver if you so wished.