There in lies the rub. Technically it is the drivers responsibility to ensure his vehicle is insured. And that is LV's position.
In the context however - an existing customer renewing insurance (albeit with the hiccup of having to begin a new contract so as to get their advertised online price) - in the flurry of the usual letters and emails that followed the call, I failed to do as you say (i.e. check for a document of insurance and a DD deduction from my account).
While this may seem an obvious error, bear in mind I recieved a flurry of various renewal letters, insurance documents, T&Cs letters etc which in retrospect related to the "just renewed and then cancelled" policy, rather than the 'start again with online price' policy.
So it boils down to what is reasonable? Is it reasonable for me to need to check every document from LV after I had been assured on the phone call that payment would be taken? As an existing customer they had taken money out of my account every month since 2014, so why would I assume there would be a problem?
I'm not entirely sure...