I should imagine that a file is created when you are registered at birth which will contain any relevant info such as health care then education then work/taxation then ultimatly your death.
It seems logical for you to be issued with a N.I. number at birth for you to have access to the health system even though as a child your not paying in to that account and thats why you are not told about the account because you have no way to contribute to it until you turn 16. you are then issued a N.I. number on a card. This will be so you can pay your contributions no matter where you work. Its like a paying in number at a bank.
Again i would think that the account is being paid into from birth to cover various things that a child will need until they reach 16.
The department that deals with the N.I. works out in advance what it will need for next year and adjusts peoples contribution amounts accordingly.
Any surplus is invested or loaned to the government.
http://www.southwark.tv/spag/spagNIFund.asp
http://en.wikipedia.org/wiki/National_Insurance_Fund
http://www.archive.official-documents.co.uk/document/cm45/4573/4573.htm