"Just deny it" brilliant, absolutely brilliant. So you'll be in court and you'll still be minus your no claims! Some people would be better off saying nothing.
I'd also add whiplash can happen at any speed, the damage is irrelevant, i'm betting I could find something on their rear bumper that constitutes damage.
The fact is the accident was your fault. It's up to the doctors and your insurance to prove there was no damage and no personal injury. If they don't want to challenge then they believe you were in the wrong.
What would be the point in them spending 10k in legal costs to save themselves £1200 in personal injury payment. It is true that there is no investigation needed upon a doctors report, the book tells you the guidelines, £1200 is minimum payment, losing a finger etc is more. There are set prices as mental as it sounds.
Oh and whiplash truly can take time to settle in, ie the next day. I have no doubt they are at it but my above points stand.
I you had been paying attention this would have been avoidable. Probably too busy updating your Facebook status on the way for a mental Nandos.