If you are really telling the thruth then i say contest it. whilst it was your fault, you shouldnt pay stuff you didnt damage. the problem with contesting it is that you want to settle outside of the insurers it seems....
I have a four hundred pounds excess on my insurance, so in theory I shouldn't need to involve the insurance. It really was the minorest (is that a word?) of taps! Every time the phone rings I'm ducking for cover....