In the UK there is no equivalent "document" per se which states this number ( although there is a plastic card which states it, you are not usually asked to produce this card ). It is a number which everyone has and is used for dealings with the Tax office ( Inland Revenue ) and other Government bodies such as pensions and all types of state benefit, unemployment benefit, sickness benefit etc etc. Hope that helps.

Monthly pay slips will have your National Insurance Number quoted.