Insurance claim Rejected due to alternative driver

I had an accident with my mother's vehicle on 18 June 2020. Due to the lock down and me working flexi hours, and my mother being on pension, and afraid of the covid-19 virus, She did not use her vehicle at the time as she stayed home as far as possible. She gave me permission to use her car to go to work, as myself and my husband worked different times. she was under the impression that the insurance is aware that i (her daughter) will be using her car from time to time, as she told them on a telephonic conversation before, that her daughter will be using her car when needed. the transcript of the call is available from Auto & General. Although she did not make me the regular driver, as this is not a permanent arrangement. Her insurance rejected the claim because I was the driver at the time of the accident. See attached rejection letter. However, when we registered the claim, they said because my mother was not the driver, the excess payable will be double. Now they rejected the full claim, The driver who caused the accident, does not have a valid drivers license or insurance. (3rd party was at fault) I feel the outcome of the claim is unfair as my mother mentioned me to be a driver from time to time, rest assured all is in place. She never missed a premium and all premiums are paid up to date. The accident wasn't my fault, and the 3rd party doesn't have a valid drivers license or insurance