It is a form of mildew or grey mould, caused usually by dry conditions. Try to keep it regularly watered and I expect it will outgrow the disease. If you want to, spray with a copper based fungicide like Bordeaux mixture.

Thanks Bertiefox, I have watered regularly, I suppose it's possible that for some reason this has been bypassed. I have two other dahlias, the cactus one also has mildew, but d. arabian nights is totally clear. This is my first year with dahlias, apart from the bishop which I just left in the garden and it survived a few years. I had no idea that mildew could be a problem, I hope it will outgrow the problem as it's rather lovely:-)