As the fault drivers insurers have accepted liability and offered to repair your vehicle, this option is worth considering - they should use reputable repairers but for added security/peace of mind, I'd ask if their repairer has any accreditations (i.e. are they PAS 125 approved, which is a recognised standard approval). You also have the option of using your own insurance company and not be referred to ‘their’ non fault specialist. However this will usually result in you needing to pay your policy excess for the repair, before being able to recover this from the fault drivers insurer. I hope this helps!