Rain penetration on top of cooker vent

Check for overflowing gutters, gaps in pointing and holes/gaps in roof.

Water can run down through the cavity insulation.

There are roof repair products you can use on wet surfaces.

Strong winds can blow water across cavities.

Is the horizontal duct installed with a slight fall to the outside so that water runs that way? Even if it is strong winds can blow water uphill.

Try some sealant along top surface of the outer cowl/wall joint.

More likely to be water running down the outerwall and then across the top of the ducting

The wall ties cannot drip water if you have cavity wall insulation

That ducting slopes downwards towards the inside of the house. So two options

1. aim the vent downwards towards the outside
2. Silicone

Certainly had some of them - but judging by state of the piece of hardboard below the duct it has been a long-standing fault.

No - it slopes inwards

Yes - took the cowl off the wall and put new silicone all round.

Also - as test - put duct tape across the cowl opening (which is at the bottom) so will see if that makes any difference.

Well spotted guv...

Thinking 2 - and/or expanding foam?

You need to stop the water where it's coming in. Expanding foam will likely only divert it to elsewhere.

You should also chip away the hole below the duct in the outer leaf and bend it down so any water runs outwards. Stupid person that done the installation as it is in the first place.

I notice there 2 pipes there hot/cold? Could that be causing condensation, just guessing.

That's where you are going wrong. The water is running down the inside skin of the outer wall and then across the ducting (as it slopes the wrong way).

You need to remove the rectangular ducting and put a bead of silicone across the top of it just where it sits itside the outer skin. That silicone (when cured) will then push the water back to the front of the ducting and back down the front of cavity.