road traffic accident

Involved in rta on Friday. Other driver pulled out of intersection on dual carriageway and crashed into front driver side of car.
We stopped and other driver pulled in a short distance in front. Damage to driver's door meant my husband unable to exist car so I got out to exchange details and other driver drove off. Phoned police who arrived and took details of accident and witnesses's (2) name and addresses. Our car was immobilised and had to be towed away. Police later received a call from other driver stating he had been in accident and that we had been driving with no headlights, we had a small black car and we had also sped away from scene!! We drive a silver vauxhall astra (older model - large) and police advised us to turn off headlights and leave hazards on when they arrived at scene. Other driver not accepting liability and trying to blame us. Insurance company cannot go any further with claim because of this. We need a car as my husband works night-shift but cannot get hire car until claim sorted. Police have advised that it will be up to CPS to decide whether or not to prosecute but did'nt think it was in public interest but we can prosecute if so wished. We feel as we had our 7 month old in the car and other driver drove off without any concern about people being injured and blatently lied to police that maybe we should take this option. We also want to know if it would be better to use a private solicitor or insurance company's (reviews of their's not very good). Any advice greatly appreciated.