You wait for APCOA to send you a Notice to Hirer, now they have your details. Do not reply to the Notice to Keeper, which is not addressed to you, but presumably has been sent to you as a courtesy and for information.
When you receive the Notice to Hirer, it will not include the mandatory additional documentation described in
https://www.legislation.gov.uk/ukpga/2012/9/schedule/4 paragraph 13, specifically
(a)a statement signed by or on behalf of the vehicle-hire firm to the effect that at the material time the vehicle was hired to a named person under a hire agreement;
(b)a copy of the hire agreement; and
(c)a copy of a statement of liability signed by the hirer under that hire agreement.
Plus the original Notice to Keeper, even though you actually have this anyway, because APCOA won't know this.
so you appeal then to your NtH stating that the driver has not been identified and that APCOA has not complied with the requirements of PoFA 2012 to transfer liability to the hirer of the vehicle.
The time limits are described in the legislation:
14 days to notify the registered keeper
28 days for the registered keeper to provide details of the hirer
21 days for the Notice to Hirer
which I believe ends up being 8 September at the latest.
Clearly another appeal point to the NtH will be that you paid for parking. You never know, APCOA might even accept your appeal.