Your wife will need to write down as much information as she possibly can about her previous employment -
Employers name and address
Date of employment
Her full name at that time if different.
She will need to do this for every job she has had since leaving school. If she doesn't have exact details, rough estimates are better than nothing.
Is she has been in receipt of child benefit, unemployment benefit or sick pay of any kind, the dates need to be included.
When she has as much information as possible, call the HM Revenue and Customs (NI contributions) Office.
Give the NI number shown on her payslips and the other number.
If she doesn't get satisfaction, get her to write a letter of authority so you can act on her behalf, and take all the information to the Citizens' Advice Bureau. Of course, if she feels up to it she can deal with it herself.
Good luck to you both.