Hello, I am a solicitor with 20 years experience. I will try to help you with this.
The relevant bit of law is set out below.
Road Traffic Act 1988, s 170
Duty of driver to stop, report accident and give information or documents
170.—(1) This section applies in a case where, owing to the presence of a mechanically propelled vehicle on a road or other public place, an accident occurs by which—
(a) personal injury is caused to a person other than the driver of that mechanically propelled vehicle, or
(b) damage is caused—
(i) to a vehicle other than that mechanically propelled vehicle or a trailer drawn by that mechanically propelled vehicle, or
(ii) to an animal other than an animal in or on that mechanically propelled vehicle or a trailer drawn by that mechanically propelled vehicle, or
(iii) to any other property constructed on, fixed to, growing in or otherwise forming part of the land on which the road or place in question is situated or land adjacent to such land.
(2) The driver of the mechanically propelled vehicle must stop and, if required to do so by any person having reasonable grounds for so requiring, give his name and address and also the name and address of the owner and the identification marks of the vehicle.
(3) If for any reason the driver of the mechanically propelled vehicle does not give his name and address under subsection (2) above, he must report the accident.
(4) A person who fails to comply with subsection (2) or (3) above is guilty of an offence.
YOU mst report it wihtin 24 hours if you do not stiop at the scene.
If you feared for your safety because of the conduct of the 2 people in the other car that could amount to a defence and you were arrested before 24 hours had expired since the accident yo may well have a defence.
I cannot comment on the strength of the evidence against you and so con not say whether you should plead guilty or not. On the basis of what you say you might well be not guilty though and should certainly think about contesting the case. There is a potential prison sentence for this offence so it would make sense to seek the advice of a lawyer face to face in the orthodox way.