Confusion over claim

I would like clarity- I had a budget policy for my car. Premium was due on the 15th of each month- are these premiums paid in advance and since my premium is on on the 15th am I covered for the next 30 days until the next premium due date? This is because budget asserts that they are not liable for a claim occuring on the 13th of august although the last premium was paid on the 15 of July- the preceding month. The incident occured on the 13 of august and the insurere was alerted of the incident on the same day. A claim number was issued on the same day and the outcome was communicated 2 days later on the 15th which was a write off. My question is am I coverd for the incident if the last payment was on the 15th of july