Accident shortly after a telephone insurance certificate!

Hello all, I am currently very worried about the insurance cover. I quit the old insurance for the new year by phone on the end of the day, I know, very late. I received the application by e-mail on the same day. On the phone the lady told me that the liability protection applies from now on, Kasko and the rest only from policy. Of course Jetz comes the way it shouldn’t. A few hours later I caused an accident, after the gas cable train got stuck on the car and the car was fired. Big question: Does the insurance pay the opposing damage? After all, they didn’t even have the opportunity to debit the insurance fee or send me the insurance contract. Maybe someone has similar experience and knows. Thank you!