Hey,
If your husband works for a large IT company ...and you are residents here.....so I take it for granted you guys are not like irregular immigrants and he has a regular and normal work contract, I guess his company would have a proper HR department, if not a relocation team, able to help you ??
I am not sure any company can legally employ someone without a NI number so did you check on the salary slip for "numero de securite sociale" ?? on the work contract ?? Anyway if you work legally you pay for the Social Security so you should have a number. I suggests you Social Security Number Search Tools for preference.