Hi Phil,
Like the others have said, my first port of call would be how the engine/gearbox is mounted, especially if the vibration is present when stationary with the engine running.
The rubber engine mounts are usually first to fail but as BDA says, the steel extensions and where the mounts themselves are bolted on the chassis. My chassis developed rust in that area and was quite thin, not normally seen because it was on the wheel arch side.
It's also worth checking the security of the two braces to the crossmember while you're there although I doubt those would be such a big deal.
Then move back to the gearbox mounts. Sometimes the steel insert disbonds from the rubber but for me that didn't give a lot of vibration, I only found it when I was pulling the car apart
If the vibration is not present when stationary but only when moving then I suppose anything in the rear suspension could be at fault, lower link bushes/UJs/radius arm front mounts, etc. That's not very helpful I know but I'm afraid it's just a case of plodding through a checklist until you find the culprit.
Brian