this is from the policy booklet for axa, i think you're grand

9 Getting our claims costs back
If we think someone else is at fault for a claim that we pay, we may follow up
that claim in the name of anyone claiming cover under this policy to get back
the payments that we make. Anyone making a claim under this policy must
give us any help and information that we need.

If, under the law of any country in which you are covered
by this policy, we have to pay a claim which we would not
normally have paid, we may get that payment back from you
or from the person responsible.