When you got into the car, did you even think for one moment that you were uninsured? If so, then I doubt you would have speeded. Did you go for a quick spin around the block or go for a proper drive somewhere?
If Mitchy is correct, then Id be very worried myself If I were you, and the fact that you havent replied to this thread might point to his sugestion being true! Whenever I drive uninsured (ie- taking someones car out for a quick spin at a meet or something like that) Im very carefull indeed and only go once round the block! It does anger me to think that some people drive everyday with no insurance when I (well ok, my Dad!) pays £1300 a year.
HOWEVER, if what you are saying is all true... keep all your internet history and if push comes to shove, maybe use this to show that you did try to/thought you had insured your car. Also, my Dad said that the internet sites (eg Tesco, Esure, Elephant) keep a record of the people who try to insure their car with different things. When I looked online for insurance in my name I tried it with my dads name, mums name, declaring my accident, no claims etc on the policy and off it to see how it altered the price. He said that when you submit it to get a quote they can see what youve done, so when it comes to actually getting the insurance they may want you to ring them so that they can make sure that you are telling the truth on the policy!
What that all means for you is... there should be some proof of you doing something or other on their site, and that might help you greatly in the end... however youd still get the fine for the points!!!
Sorry about that, didnt realise how much id typed!
-Phil-