same thing happened to me just over a year ago
sat at a set of red lights and guy behind thinks they have changed and set off driving up my rear end of my scooby
any way insurance said he is insured so i had my car repaired and paid my excess only to find out the guy was not insured and it was down to how long it takes to update the system ie months
,the guy had took out insurance and taxed his car on it then cancelled it or never made another payment.I have been waiting over a year to get my money back as i had the work done by a friends grg who i knew would do the job spot on as he makes show cars
.
a fooking year to get money back its a fecking joke had a claims firm on it for a year now as my insurance want the money back too as they everything over my excess
good luck