Saxo VTR 1999 - Vibration and Rumbling

Noticed a vibration at 50+ mph, got wheels balanced (centre-less alloys - that's another thing entirely!) and this hasn't solved the problem. Doesn't seem to disappear when I try to "drive through" it either.
Even comes and goes when I maintain similar speeds?!
If this isn't a balancing issue, what could it be? There seems to be a random rumbling from the front end also when I steer any large amount at higher speeds - is this related?
Just bought the car and don't want to go back to the garage and not know what I'm talking about. Any help / guidance appreciated.
Thanks, N!

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