Conceptually, that seems sensible as an economical method to resolve such issues.
I would see a problem with such a tribunal assessing legal liability. Specifically, you can imagine the objection to such a process on the basis that it would usurp the jurisdiction of the courts. Constitutionally, the High Court is the court of original jurisdiction whilst the courts below it operate on delegated jurisdictions. Other quasi-judicial entities also operate on specifically created authorities. I cannot see the jurisdiction of the courts being ousted for matters such as this.
In relation to the more serious and complex personal injuries cases I would not be too happy for them to be put in front of a tribunal for assessment of damages as I would have concerns about competence. To ensure adequate competence to judge such matters you would nearly have to create a parallel judiciary. In passing I might observe that the book of quantum does not impress me too much. There is at least one High Court judge whose decisions make references, from time to time, to the fact that they found the Book of Quantum to have been of no assistance whatsoever !