Is that a definite no? Has your CWPC been in touch with Cambridge Head Office to check?
It may be that you could still do the diet and take Champix so long as your doctor agrees to supervise you. However, given that you haven't got loads to lose (assuming your stats are right?) you could always try another diet if your doctor doesn't agree. I'd imagine the side effects that some people get with Champix are the reason for not recommending you do Cambridge at the same time (Nausea, Headache, Difficulty sleeping, Abnormal dreams, Sleepiness or fatigue, Dizziness, Change in taste, Dry mouth, constipation, diarrhoea, vomiting, abdominal discomfort or bloating, indigestion).