I was given my National Insurance number because I was able to prove how diligently I was looking for work. It didn't take even a month, whole thing from call to appointment to getting the number in the mail. And just got my "real" card in the post last week.
That said - the guy who did my interview did tell me that (in my area, at least) he had found that people looking for work WERE being discriminated against if they didn't have a NI number already. So he told me that I should keep my "receipt" that I had applied to show prospective employers. Got my number so quickly, it really wasn't a problem.
I think, like elle said, it's probably very regional what employers will and won't do. I did think it was going to be very chicken-egg, too, but got lucky I guess!