1. Did you buy the car with a statutory Warranty?
(understand that those "extended warranty"/ "free warranty" etc things are usually insurance products, and not warranties)
2. Your insurers will probably treat this claim as a driver-at-fault accident.
That means that, at least, you'll be paying the excess on your own claim.
And of course, your next premium will be through the roof.
3. As to what you'll need to persuade your insurer that it was not your fault, you'll need to ask them.
If I was handling the claim, then at least, I'd be looking for a report from a Mechanical Engineer - something from a local retail mechanic may not cut it.
They may also want to have the car examined by their own technical people.
But you'll need to ask them first hand.