You sir they have over a barrel and they are reaching for the Vaseline.
You have provided false information. If they know this they may refuse your claim. If they chose to do that good luck getting insurance without lying on the application where it asks "have you ever had an insurance claim denied".
If your insurance company gave you the flick when blame was apportioned name them, shame them and change insurer. They insure you and are supposed to pay you out and seek restitution from the other party or their insurer.
Or were you hoping to not lose your excess by leaving your insurer out of it? If so change your insurer. Most reputable companies have no excess for no fault claims.
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