Hi hush33
My white smoke problem was put down to the "air fuel ratio sensor" in the exhaust. It intermittently cut power to the MAF and so it injected more fuel. Mine only did the smole thing in winter, or should I say below approx 8 degrees. I no longer have the car so I can't say for sure it fixed it. But it did fix it while on a live test at Lexus. Originally the cars engine tone changed and it also put out a puff of smoke, after the new sensor was fitted it no longer had the symptoms, do I assume a fix.
It's not a cheap part, over £300 from memory fitted at Lexus, and of course the hour and a half live test to diagnose the problem. But I have to say, Lexus Bristol were awesome despite not being able to diagnose why my car had a P0093 fault. Although I fixed that myself, lol