Research online indicates that if the VVT pulley is failing, it tends to go quiet when then VVT solenoid electrical feed is unplugged. Mine doesn't; the rattle is the same both with the solenoid connected and disconnected.
What matters is that the engine has stood still and gone cold. If still warm, there is no rattle.
Careful listening with a stethoscope indicates that the rattle is coming from about four inches along the exhaust cam from the pulley end.
My conclusion is a lazy hydraulic lifter bleeding down and then needing to be pumped up again.
Other thoughts?
I have put a video
here.
The engine is started ten seconds in.
Ignore the water; I'd just carefully degreased and then rinsed the cylinder head whilst I had the plastic cover off.