Does an employer need to register as one?

I am preparing a small SA return, and found out my client has taken on a part-time employee @ £50 per week, he's a student.  She's been paying him since last April and hasn't registered with HMRC, I have only found out now.  My question is, does she need to inform HMRC? I'm asking as I remember speaking with an HMRC technician a couple of years back when I took on a client with a late PAYE return, he had 1 employee paid £75 per week. The technician told me they did not need to know about him, and he didn't need to register as an employer because his employee's wage was below thresholds.  I found this a bit off as in theory, it could have been a second job subject to BR income tax (it wasn't, but you get my meaning). Could any of you smart people clarify this? I know it is a hectic time of year, but if you could take a minute it would be much appreciated, I'd rather not create any more paperwork than I have to.