Hmm
I have the greatest of respect for Ethel (who is one of AB's finest contributors). However, I can't agree with Ethel's answer.
Let's try an analogy:
Suppose that the other driver had (as a result of negligence), instead of colliding with your car, gone off the road, crashing through your garden fence and damaging the wall of your house. You'd have been entitled to claim against the driver (and, ultimately, their insurer) for the full cost of repairs to your fence and house. It would be completely irrelevant as to whether you had property insurance or as to what the excess might be on any such insurance.
As I see it, you're now in a similar position. i.e. your claim is against the other driver (and hence against their insurance company). Your own insurance policy is completely irrelevant. (You'd still be entitled to make a claim for full compensation even if you'd been driving, illegally, without any insurance). Your own insurance company might be acting as your agent when making a claim against the other driver's insurer but that does not give them the right to withhold payment of any excess. However, any challenge about the level of payout should be directed to the other driver's insurer, rather than your own.
Chris