So I had a good think about this and it sounds as though the venting may be difficult to fit given the layout of the room.
I should mention there is a large double window along the external wall (not shown) which is going to limit my options somewhat.
I appreciate the advice on limiting bends as much as possible, it just makes it harder to vent the cookerhood directly.
What I think I may do now, is to core drill the wall and fit a passive ventilation grille on both sides. This works better for the following reasons:
1) it will not require the tenant to use the cookerhood, which tenant's often don't anyway
2) it will not require difficult running of the ducting, and I'm uncertain about the best way to run it.
3) it will ventilate the whole room and not just the hood, and as this is a basement flat it is likely to make more of difference to airflow.
4) it can be adapted later for ducting, or an active extraction fan if need be, without much trouble.
The tenant has recently had a washing machine installed in the kitchen where previously there wasn't one, and there is a fridge and freezer in the alcove. I suspect this is why a small amount of mold is forming on the skirting behind the appliances. It is a basement flat with a concrete floor, DPM in good condition. No signs of rising or penetrating damp, purely condensation issues from having so many appliances in a smaller, not easy to ventilate, living space. Retro-trickles have been fitted to said window, but I suspect the tenant of closing them when the temperatures drop, and I already know they close the door to the hallway routinely to trap heat into the room.
So, the plan as it stands is to core drill the wall and run a gasket (duct through it) with passive grille either side. If this does not work, I will suspect the tenant of blocking the grille to conserve heat and then we can talk about potential misuse and penalties later down the line.