How to stop rain coming down outside of flu pipe

[middleofafield]

So last year, I installed a woodburner in our house. I've done this before and worked with stovefitters in the past, so I have a fair grasp. The issue I'm having is that we are in an exposed area of Scotland, and when it rains with wind, water is coming down the chimney on the outside of the flu liner (not into the fire) and down into the fire opening where it drips down the wall making a real mess. I'm getting some scaffold set up tomorrow so I can take a look at the top. My suspision is the bog standard cowl I have fitted and that the rain is being blown into the gap between the 5" flu liner, and the 6" flu. It's not the flashing or pointing as this has already been done, and the water is only coming down the flu.

My question is how best to seal the flu at the top? Would it be possible to apply some fire cement or mortar in the gap at the top? I will most likely replace the cowl either way a belt and braces approach.

Very much open to any other ideas..

Thanks.