No. A National Insurance number will only provide a statutory excuse when given in combination with one of the acceptable documents, as specified in the acceptable document lists A and B in the guidance such as a full UK birth certificate.
Why isn’t a National Insurance number on its own sufficient to demonstrate a right to work?
The purpose of the National Insurance number (NINo) is primarily to link an individual’s National Insurance contributions and credited contributions. The NINo is also used as a reference number for individuals within the social security system. It was neither intended, nor designed to be a tool for identifying or determining an individual’s immigration status. Not all NINo holders will be allowed to work in the UK and if they can work, they may be subject to conditions.
Source: Home Office (Questions 31 & 32)
I have lived in the UK all my life and my P45/ P60 shows I have paid taxes, why cannot this be used to show my right to work?
For the purposes of the check that we've been asked to perform on you, by your employer or potential employer, you will need to provide a document that shows your right to work in the UK.
Your right to work can only be demonstrated with a document that displays your nationality and is on the Home Office checklist of acceptable right to work documents.
What document can I provide instead to prove my right to work?