Thanks for your input.
I don't have a hooded trench.
I don't have a navy coat.
I can shake off water from my Sandringham (made of cotton gabardine). This is just cotton. I tested and it didn't tolerate as much water as cotton gabardine.
But I do have already
2 wool winter trench
1 Sandringham trench
1 hooded short trench rain coat (this is paper thin - doesn't keep you warm)
1 short blazer trench
All from Burberry.
+ bunches of other coats because we have 4 seasons here and winter time is often freezing (-25C/77 F)
It's always drop dead hard to make a decision between what you need and what you want.

I want to keep it but I don't need it because it isn't made of cotton gabardine.