The OP has my sympathy. As I am one of those who hate missing planes and trains, I am normally on time, or early.

Turning to his litigation. SWMBO, who is a UK qualified and admitted solicitor, doesn't think he has a chance.
The easiest way to "check" the chance is to test it with the legal folk from the insurance Co. Both my house insurance and my travel insurance have legal help. I have used them before to check my chances of a claim. Send them the details, and the wording and get their opinion on the chances of a winning claim.