The 60mph thing is strange... defo. not happening below that?
When the lights come on, what's the car drive like? Do you have ABS? (Does the car skid without the ABS pushing back at you)
I know you won't have ESP or Traction Control; but you may still have ABS.
Have you checked the VCDS register on here? There might be someone local to you, who'll give your car a quick scan.
The ABS switch fault won't cancel on a simple ignition reset.
My guess is wheel speed/hub sensor on the way out, basically not reading the road speed correctly, which throws the other systems out of sync. Strange though, because it usually requires a re-calibration before it resets...