Hello I am a solicitor with over 15 years experience. I will try to help you with this.
The NIP must be served (or despatched so that they will arrive) within 14 days of the offence. Unless the police can argue that they have used due diligence and needed the extra time to work out who the registered keeper was or if the delay is your fault (eg if you have moved and not told the DVLA) .
Also if the police were present at the scene and gave you notice at the time then the time limit does not apply.
Otherwise this failure to serve in time will be fatal to the intended prosecution.
The car is a leasehire car which may have affected the time it took them to contact me. However, for my previous speeding offence they traced me easily and quickly enough and it shouldnt have been that difficult.
They might have an argument then if it was a hire car. You will need to show they have not acted with diligence which will not be easy. You should respond to the NIP raising the late service issue. You should probably get a solicitor who might be able to use this issue if luck goes your way to beat the prosecution. You should instruct a solicitor soon so that they can get to work in advance of the hearing.