I put a meter on the centre contact and on the end of arm and there is no continuity. Is this right or does the extra high voltage overcome this ?

 

They do of course conduct electricity, as they need to, it is likely that where you put the metre probes on the arm there was micro burning, stopping the current flow.
Every time a pulse is passed by the HT system a tiny amount of depositing occurs, where material moves from the rotor arm to the HT lead contacts inside the dizzy cap, this is why they look blistered and burnt, this is normal, normal trick is to run the arms end on a tire, this will be all that is needed to clean it up, although it will still conduct perfectly anyway.
In a old points ignition system the same process occurred much more readily, you could even see the pit on one contact and the corresponding pile forming on the other if the capacitor was duff, where material had moved from one to the other in the direction of flow.
tabetha

 

I should have mentioned that I had already cleaned it so I had a good contact and I did get a small reading but nowhere near what you get if you touch the two probes together.