Mat, since you haven't gotten any help from the diesel bros, let me try. The above indicates that it happens more when the engine is cold, not hot. It's very easy to confuse white with blue smoke, as anything not black seems to be white. So check precisely.
What's the condition of the smoke: white with diesel smell and hangs in the air (vapourised diesel) or white with no smell and dissipates (steam)? If the former, it could be: injector problems, timing problems, low engine compression or a faulty fuel pump. If the latter, it could be a blown head gasket, allowing water to seep into the engine. If it's blue smoke then it's burnt engine oil. Your mechanic said maybe burnt piston rings, so he suspects this, caused by blow-by.
Since your engine is vibrating, I would suspect misfiring, and any of the above can cause it. Your car should be under warranty and BSRI, so why not send it in to a dealer to check? Avoid the dealer who said "it's normal" :wink: