The process was all very mundane. At five till nine, enough staff were there to open the building. We'd formed a half-hearted queue, but it wasn't necessary. The receptionist called our names out, one by one, and we came forward when called to be told what floor of the building to go to. On the open plan second floor, the receptionist there found an available interviewer, and he sat down to process me.
The purpose of the interview isn't to decide if I should be allowed to have a NI number or not, although the interviewer does act as the main gatekeeper in that process. Instead, the interviewer is there to fill out the application form for me - and in the process, collect enough information from and about me to put up a good case for why I should be given one.
My interviewer was a pragmatic bureaucrat, skipping over sections that I technically could have filled in, but he thought would only distract from my application. (Yes, I've lived in the UK before, but not recently. Yes, I've been a student here, but not recently. Yes, I'm applying for jobs here, but that's less interesting and less convincing than the fact I've already been employed here.) I read over all he'd filled out as if in my words - including practical notes, such as how my signature has changed since I signed my passport nine-and-a-half years ago - and signed the form. He only photocopied the most relevant documentation I'd brought with me, notarized it, and sent it all over to his colleague to double-check before I left.
In under half an hour from when I'd entered the building, I was done. I have a temporary NI number, so can be paid for the Imperial job finally, and a promise to hear back from the system in four to six weeks.
Note: It's just as well I know my SSN, since it was required for the form, as an American, and I hadn't been warned to bring it along.