Egr fault and you’d know about it, when they stick open it sounds like the head gasket has gone and smokes for england!!
Sticking shut is fine and i’ll often disable hi milers in to a stuck shut state
Look next to the air filter box for the air plenum connecting to the EGR assembly, its a ClicR clip so you’ll need pliers for, or get creative with some nippex cutters unless its already been swapped for a jubilee worm drive clip. Its a 3″ dia assembly. look if it has a vac actuated flap at the very end, see if this is remaining open when you rev, when it sticks shut it gives the same symptom as soma described for a choked air filter.
On a 05 plate it shouldnt have that kind of “flap” system, but they do fit the manifold of all these engines, so a bodge by a previous owner could see one fitted