You have a number of ways of claiming. You can claim through your own insurance, but it gets complicated. The valet was driving with your consent, so your insurer could claim through his insurer, who claim from the at-fault party. This is why they say they cannot do it, because he was not on your policy but had the provision of cover of his insurer. They avoid dealing with it because it's complicated. Whilst the valet parking service drove your vehicle, they were acting as a "Bailee" of your property, as such they are automatically liable for anything that happens to it because they have a "duty of care" over your property. Your best way of claiming is directly off the Valet company's insurer. What happens after that is up to them to sort out. The third party claim details are up to the valet company to get and deal with. The loss that occurred is still your claim though, so you are entitled to another vehicle and any out of pocket expenses whilst the claim is ongoing. Should you struggle with them, contact an FCA regulated accident management company with a good reputation and they should be able to sort it out.