I assume that by 'crashed my car' you're referring to situation where you permitted someone else to drive your car who then had an 'at fault' accident in it.. (If you're actually referring to someone else crashing INTO your car, with it being their fault, then the following won't apply).
Unless that person was a 'named driver' on your policy, your own insurance won't pay you a penny. Further, since the driver only had insurance covering damage to the other driver's car (or injury to the other driver), their insurance won't pay you a penny either.
It makes no difference whatsoever as to whether the level of damage was sufficient to cause the vehicle to be 'written-off'.
It's up to the person who was responsible for the damage to your car to pay for it. Since they've got no relevant insurance cover it must come from their own pocket. Your only option is to make a formal written demand for payment, threatening legal action if such payment is not received within a specified period of time. If payment is not received within that time you should commence a claim through Her Majesty's Courts Service's online system:
https://www.moneyclaim.gov.uk/web/mcol/welcome
However if that person hasn't got any money, or you can't sue them for personal reasons (e.g. if the driver was your hard-up student son) there's absolutely nothing you can do.
Chris