Crash due to TfL very poor bike track construction

Yeah, that's the way pretty much all companies assess claims of liability. They send you a form designed to collect the information they think they need to assess a claim. You fill it in and send it back to them. They make a decision... etc. Its a standard bureaucratic process. What were you expecting?

You're already talking about making represented insurance claims before you've even attempted the process offered by TfL. A process that so far seems neither onerous or unreasonable.

Arbitration or Small Claims will usual require evidence that you've made reasonable attempts to resolve the matter with the other party before they'll intervene so maybe try that first.