XKR 4.2 - Vibration at speed

[KGL]

My 2002 convertible has aways suffered an annoying vibration through the steering wheel at speeds in excess of 70/80 mph.The car is fitted with 20" Detroits and, amongst other modifications, was lowered by Racing Green Cars ( fantastic company by the way). It's been checked out countless times by the supplying UK Jaguar along with stories about XKR steering being very sensitive,low profile tyres, car being lowered etc (which I'm told doesn't affect the car) - but all to no avail.
Does anyone have any similar experiences and hopefully some useful advice.