Sounds to me as though you have a buckled wheel..

It did cross my mind but would it not still vibrate/wobble no matter what side it was on? Range Rover Sport 2010 3.0 TDV6 HSE in Black
103,000 miles and a BAS Remap

Did you swap sides or front to rear ?

I don't know as the only way I could tell was that one wheel had a very small kerb mark on and that is how I know it ended up on the wrong side after the first trip to the garage. The other wheels, they have no distinguishing features, I have no idea if they were front/back or side to side or both.
This wheel is now back in the exact same position as it was originally. A couple of things confuse me.
The tyres are approx 700 miles old and the alignment was done via a hunter machine at the time.
If a wheel was buckled would it not have done it before/still do it?
Although I am pleased it is fine now it does intrigue me as to how by rotating the wheels that it caused such a problem.

Cheers,

Chunk Range Rover Sport 2010 3.0 TDV6 HSE in Black
103,000 miles and a BAS Remap

It depends where you were feeling the vibration, if it was through the steering wheel then moving the buckled wheel to the rear of the car will pretty much hide the issue (if this is the case, when it was on the front you only felt the vibration through the wheel), if you have directional tyres fited and they're running the wrong way they MIGHT cause vibration, but I would doubt it.

Try swapping the front to the rear one side at a time, that way you can pinpoint which wheel is the problem. Or have the wheels balanced and ask the fitters to check that the wheels are running true.