I just checked on Wikipedia and the scheme started in 1948.
The Department for Work and Pensions holds all information about the allocation of NINOS,but this is not available to the general public because it is confidential. The NINO of a person will not really help you with your research because it is used only by certain UK Government departments ie HMRC, DWP, Child Benefit and tax credits to etablish the identity of a person claiming benefits .A person's NINO is not recorded at either birth, marriage or death so it is not much use.
You can search Ancestry for all records of birth etc. Hope this helps. Denise.