Sorry to hear about your dad. You shouldn't need to pay a fee for the medical certificate of cause of death, so don't worry about that. However, if you're planning a cremation, you can expect to pay £82 each (£164 in total) for the Certificate of Medical Attendant (Form 4, filled out by the doctor who was caring for the person who died) and the Confirmatory Medical Certificate (CR5, filled out by a second, unrelated doctor).
These two forms essentially confirm that firstly, there's a record of the circumstances surrounding a death and that secondly, that the record given by the doctor caring for the person who died was accurate. Your funeral director can arrange these.