You will for most jobs need to apply for your ni number yourself.
If you search on here there are details of the call centre you need to call who will arrange an interview so you can get a national insurance number.
Its far easier to apply for a ni number once you have a job but if you dont have a job if you can prove your wife is looking for a job (ie letters saying thank you for you application but no thanks from companies and/or showing your registerd to a job agency)
Companies can employ you with out a ni number my wife got a job at a coffe shop and they just used her dob and sex as temp number. What they were more intrested in was her passport with visa, and a bank account.
As if they employ a person with out the right to work in the uk they can get fines of a few thousand quid!!
Maybe worth looking for a part time job where people are happier to except without ni number gain the ni number and move on.