Just a follow up to an old thread (Google groups won't let me post to a thread more than one month old) -
My father in law and I replaced our old hot water cylinder as the tests you suggested confirmed that a dodgy coil was to blame. I was even able to use the cylinder that he had taken out of his house to have a solar hot water system installed so it cost next to nothing.
So far everything seems to be working satisfactorily.