Engage with the client and explain the reasons for your decision in line with your pre-determined process. It is very important to have a process in place before you receive a complaint.
Complaints even if they are not justified can eat up a considerable amount of resource both financial and time if they are not handled well.
If the complaint is from a consumer – a person acting for non-business purposes then they have specific rights under the Consumer Rights Act and you need to get the process right. ADR is now a feature that must be taken into account.