This problem has crept up on me over the past month or so, and now seems to have stabilized without getting worse:

When firing up the engine in the morning, there is a pronounced mechanical 'clatter' and the engine rocks/shakes for a couple of seconds before settling down to idle. The whole front end of the car shakes too.

I'm wondering if this could be the engine mounts? Or perhaps something related to the timing chain?

Secondly, the exhaust seems to be emitting white smoke/steam while the revs are high on start-up/warm-up. There's no visible exhaust emission for the first ten seconds or so, and then white smoke appears. After a few hundred yards of driving, the smoke disappears.

The smoke doesn't smell of antifreeze: just a slightly rich exhaust. However, my coolant levels have always dropped a little over time, needing topping up every month or so.

Could a little coolant be leaking from somewhere overnight, and then get burnt off in the first few seconds after start-up?

Suggestions welcome!