That sounds rather like a loose steering rack (check the U bolts as above) or, very likely, broken front subfreme rear (toeboard) mounts. The rubber often seperates from the metal, but it is not too obvious. It eventually results in structural cracking in the inner wings, because the subframe moves around and transfres abnormal loads to the front teardrop mounts. I agree with Cooperman, get rid of those lousy rubber mounts, but do them all, not just the toeboard mounts, or again things will crack.
It is likely that the subframe mount problems will be causing your vibration too.
Your final drive ratio should be 2.95, nicely low for relatively quiet and economical cruising at motorway speed. You do lose a bit of acceleration, but the City E engine was mildly tuned, with a larger carburettor and higher compression than some 998s to give a bit of extra torque. I had one and found the performance to be adequate, and the economy fairly good.
But do, very urgently as has been said, check the steering column to rack clamp bolt, and the column splines. Failure there used to be common, when the Mini was quite new, due to lack of proper maintenance by inexperienced garages or owners, and killed at least a few people. I see signs on this forum that the early knowledge has been largely lost and problems like worn splines are happening again. We don't want to see anyone killed. The clamp bolt is supposed to be checked for tightness at every service. If it has been loose, and the splines are worn, you will need a new inner column, clamp bolt and locknut, and you must use the correct nut and bolt, not any substitute that seems to be right.
Please also be aware of the very important procedure when refitting the steering column after checking the splines. Both rack U bolts MUST be loosened, so the rack is free to rotate and align itself to the column, otherwise rapid failure is inevitable.
Sorry to seem to labour the point, but we don't want any forum member to be killed. Someone will be, sooner or later, by failed steering splines, but at least here we can do something to try to prevent it.
Edited by tiger99, 11 September 2012 - 08:05 PM.