Even with my limited recollection of PI work and more recent horse related injuries (so no one to sue) recalls to mind that it can take a few days for the pain to start and a couple of weeks for it to manifest itself in earnest, even if the victim is a person who knows their rights and where to find a solicitor.
Really, insurance companies would pay less out if they actually fought the claims they considered dubious rather than giving in e.g. on knock for knock. I remember being furious when our insurance company did that for an incredibly gentle nudge of the car in front in static traffic (by my husband of course) The driver in front assured us he hadn’t felt a thing and all was fine... until he realised he could get a few quid. We railed against the decision but the insurer paid up anyway.
AXA even want you to include evidence of medical injury at the time of claim - have you tried seeing your Dr within 3 days!? Come on, play fair. Defend the fraudulent claims and pay fair on the real ones. Whiplash can be a real pain in the neck... but can cause long-term damage and certainly can be extremely painful.
Meanwhile the success the insurance lobby have had in the Legal Aid Bill which will cause so much damage in other areas of public interest, should be enough for them now surely.