The driver who braked (but was not involved in the accident) is irrelevant.
As FP has said, the usual procedure is that the person at the back of the line, who struck you, and then caused you to strike the vehicle in front of you, is held liable.
However, your case may be complicated by your lack of insurance - for example, the hire company can't hire out their vehicle, so will be coming after you for the money they'd usually be earning.
You may need specialist legal advice. The sort you pay for.
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