As you know BE, I've already posted up info regarding REIN and the legalities surrounding it. To get a first hand idea of what it sounds like, tune your radio into 612Khz on the MW scale and drive under a high-voltage electrical distribution cable, the ones that are attached to the large pylons.
It is akin to your description below, but it's more of a buzzing noise than a hum. Bear in mind REIN is everywhere, just drive around like a saddo (me) with your radio on the frequency mentioned, and you'll hear it regularly and sporadically. It depends on the level of 'noise' as to whether it's service-affecting.
What Josh describes above is perfect for fault-inducing REIN. IE- The circuit will reset to it's 'max' but DLM will drop it down due to high-error counts caused by REIN. This is assuming that the D-side cable has been PQT tested and has an AC Balance of >-50dB. I personally think it should be above -60dB or even -65dB, but the REIN team will take the case on -50dB or above.
With minimal REIN interference on ADSL, we can fit an RF3 filter which when coupled with the SSFP will halt the REIN in its tracks. Now, I'm not sure if this same product will work on VDSL and its higher frequency band-plans
HTH a little,