Can my car insurer choose NOT to automatically renew my policy, even though I pay via Direct Debit?

I have been stopped by the policy today (23rd Jan 2013) for driving without Car Insurance which made me feel sick at the shock of this being the case. Fortunately, given the circumstances that are explained below, they looked in favor of my situation and let me off with just charge to recover my vehicle from a local recovery yard when my car was seized at the time I got stopped.

The situation is this...I was stopped by the policy for driving without insurance. It would appear that the insurance company had ended my policy at its annual anniversary on 16th November 2012. The insurance company or should I say broker (RescueMyCar.com aka NCI Insurance) claimed that they attempted to write to me 3 times but had no response from me. However, I had previously informed them back in April 2012 over the phone that I had moved address, only 1 mile down the road, this was evidenced by the fact my driving license that was issued to the police beared my new address and I was indeed the owner of the same vehicle. However the insurance is claiming to have had no knowledge of my call to inform them of the change and had not heard from me since I originally took the policy out in November 2011.

Meanwhile back at the Police Station, the officer informed me that I have a case against the insurance company to recover my loses. This is on the basis that given I pay via Direct Debit and as the Insurer was aware, I had not informed them of any material changes in the last 12 months. Therefore a new policy could and should indeed have started even if they had found an alternative provider within their brokerage. Furthermore, given I did not reply to their correspondence like most insurance companies/brokers would have assumed I was happy to take out a new policy with a new seemless Direct Debit.

I have to also point out that the company still had a valid mobile no. and email address. In fact I checked my Google Account and they had in fact emailed me 8 times in the last 12 months but none were to attempt to make me aware of the insurance ending and no subsequent renewal. All the emails were just simple marketing letters. For the really serious stuff, they just relied on good old fashioned post and none of the more modern methods of communication. I fully appreciate that I too have a duty to check my bills and direct debits but who really does as long as they are getting paid, furthermore companies soon get in touch when they are owed money, I would have thought an insurance company would have been more than keen to pick up the phone and offer me a renewal quote.

So with all the above, can my car insurer choose NOT to automatically renew my policy, even though I pay via Direct Debit? and knowingly put me at risk of driving without using all methods of communication to inform me.