Re. the 'old' part of your post:
Just a practical driving note to start with:
Every time you come to a halt in traffic, even if momentarily, you're meant to apply the handbrake. In a 'stop-start' queue that could mean putting it on and off at least ten times per minute for several minutes in a row. (And yes, before you ask, I DO do it myself!). That way there's no chance of you rolling either forwards or backwards!
Further, when stationary in a queue you should always try to ensure that there's a full car length between you and the car in front. That way you're unlikely to be hit by a car rolling back a few feet as the driver sets off.
Having got that out of the way, if everyone 'exchanged paperwork' for minor nudges our road system would probably grind to a halt. While driving in central London, I've had three different black cabs run into the back of my car (with minor 'no damage' nudges) in the space of twenty minutes. Nobody stopped, and I wouldn't have expected them to.
Now to the newer part:
The law only requires you to stop and 'exchange details' (or report the accident to a police station within 24 hours) if there has been injury to someone other than yourself or to 'any horse, cattle, ass, mule, sheep, pig, goat or dog', or if there has been damage to another person's property (including, obviously, their vehicle). If you had a well-founded belief (based upon the fact that the other driver didn't even bother to stop) that no such injury or damage had occurred, it's unlikely that a successful prosecution could be brought against you either for 'failing to stop' or for 'failing to report'.
Further, I can't see (based upon your account of things) how the CPS could possibly obtain a conviction for 'dangerous driving'. That's a very serious charge, with a high burden of proof which requires evidence of a SUSTAINED action. (i.e. a momentary lapse of attention CAN'T result in a conviction for 'dangerous driving'. Only the much lower charge of 'driving without due care and attention' could be brought).
I'd recommend speaking to a solicitor BEFORE responding to the police letter (so that you don't accidentally write something which could be construed as admitting guilt) but not worrying too much about it. The very worst outcome I could foresee might possibly be a conviction for 'driving without due care and attention', resulting in a few points on your licence and a small fine but even that, with decent guidance from a solicitor, is probably unlikely.