As it isn't a local authority ticket, they have to rely upon normal contract law principles to enforce as they have no statutory powers (unlike the Local Authority). In other words, they will be claiming that you agreed to the additional parking charge as you contracted with them when you left your car in the car park. However, under contract law any additional charge must be a genuine estimate of their loss (liquidated damages). If it is more than that, it is an unlawful penalty charge In this case, £50 is not a genuine estimate of what they have lost so it's a penalty charge which they cannot enforce.