Hi Gavin,
If you've had it into a garage twice, it's surprising they didn't check this out for you properly. Too many things could be giving you the issue, and it's a process of elimination.
First I'd be checking battery and connections. If coils have been done, then starter motor and also making sure fuel pump is working. The white smoke could very well be a coolant leak. Defiantly something any decent mechanic would diagnose and sort you.