Help!! What I will describe only happens periodically, perhaps 4 or 5 times a year but only on long journeys with a good speed limit in force, ie: on motorways.
Last year after about three hours travelling the steering started shaking at about 70mph. It gradually got worse and when I braked gently the whole car shuddered with the steering wheel literally shaking violently. After a while it calmed down, was ok for another hour but then did it again.

That was about about a year ago. The car Range Rover Sport 2011, went to the dealership a few weeks ago couldn't see any problem but mentioned the discs and pads needed changing and the from tyres were worn on the inside. So, since that visit, new discs and pads on both the front and back, new tyres on the front and a full wheel alignment. I thought the problem had been solved but last weekend, after a three hour run on the motorway the vibration started which I could feel through my feet, then the steering wheel started shaking and when I braked, the car literally hopped around the road and the steering shook like ! Slowed down then it all became ok and has been ok since. Any clues you clever folk out there? My thought is now a very worn bearing somewhere which, when it gets hot on a long trip starts to fail, badly. Thanks for any advice.

Sounds like a brake caliper may be sticking on sometimes.
Next time it does it pull over and see if any of your brake discs are hot. You will probably see some colour distortion with the heat if this is the case but be careful if you do have a feel as if a caliper is sticking they get seriously hot.

Many thanks for taking the trouble to reply. It's a good thought but the car drives in a complete straight line with no wandering left or right at all even when the problem occurs. It's going for an mot soon and I have an extended warranty that covers pretty much everything so it might be a good start. Thanks

No problem.

I did have a very similar issue before, not on a range rover but a jag. Anyway same story was usually fine but on the occasion the whole car would vibrate. Turned out to the a front caliper sticking but only sometimes not everytime. Again only came to light when i pulled over and realised the front driver side brake disc was smoking.

do you have the cruise control on when this happens

+1 for the sticking calliper...had this happen before... The car will give you no indication of a brake binding I.e. Pulling to one side... Car will drive completely normally... What happens at normal speeds the brake disc and pad can dissipate the additional heat relatively easily but at motorway speeds the heat builds up so much that the disc starts swelling with the heat and hot spots on the disc cause it to start oscillating within the carrier hence the shaking steering. You pull over and it doesn't want to move. You leave it five minutes or so and you can drive on as if nothing had happened...( because the disc has cooled sufficiently and almost returned to shape) five minutes further up the motorway the problem will return...
I had tried cleaning up the carriers but to no avail....
A new calliper cured the problem....
If testing this just feel the outer rim of the wheel.. It will be hotter than the others due to heat transfer... Never ever touch the disc or you'll lose your finger!

The above is correct

You should be able to feel the hear difference just by placing your hand near the wheel, but an Infa Red thermometer can be picked up very cheap