do we have any grounds to appeal this as we were not the registered keeper of this vehicle?
Using strict terminology, no. The lessee can never be the registered keeper, but liability can be passed to them as 'P' who would be regarded as the 'owner' for these purposes.
https://www.legislation.gov.uk/uksi/2022/71/regulation/6/madeAdvice is tricky here because there are still 5 days left to pay the discount/ make risk-free reps and at least 19 days during which you are in charge of proceedings. After this it depends on several factors, including:
Whether you make reps, in which case the discount would be maintained until they reply + 14 days;
Was the vehicle leased directly or possibly by an employer and then allocated;
Is the lessor a national company or local. I ask because larger companies tend to deal with these issues regularly;
What action would the lessor take on receipt of a Notice to Owner demanding £70 e.g. pay in full and recharge, including admin. fee, make representations to transfer 'ownership', again including admin. fee;
What would be the marginal difference between the admin. fee and the discount(your contract paperwork should refer to the admin. fee);
We haven't seen the photos, but you seem to acknowledge that the car was parked on DYL and that the contravention occurred, however, the PCN relates to Bruyn Road whereas you've referred specifically to Salisbury Road!