I have a Galaxy Ghia TDI Auto which starts to shake when speed exceeds 40 mph. All obvious causes e.g. wheel balance have been eliminated. Is this a common fault?

You say wheel balance has been eliminated, I'd guess you had the wheels balanced off the car. It is possible (but unlikely) that there's something about one of the wheel & hub combos that means there is imbalance that off-the-car cannot resolve. I only say that so you realise it's not completely off the list of possibilities, just moved to the bottom of the list.

More likely would be something like a driveshaft vibrating, that is usually due to a failure of the intermediate bearing on the long (driver's side in the UK) shaft. Another option is brake discs, they can become out of true and the the only real fix is to replace those, as the bit that's too near the pad gets heat hardened and so gets worse even if skimmed to correct it, to check you'd ideally want a DTI as the run-out can be very small. Another option is a tyre that's not true, you'd hope the tyre place would have noticed that if that were the case, you can just jack the car up, rotate the wheel while keeping your head still, look at a fixed point so that if the tyre isn't circular your view of the fixed point will alter, then do a similar thing with your head in a different position to look for the tyre moving from side to side .After that, it's things like engine mounts.