Need a cowl to fit on to this piece of pipe

Have a look at Screwfix for a 90 deg round section plus a ventilation grille to fit the 90 deg round section

The item in the first post looks like a square to round gutter adapter. Nothing to do with a soil stack. Soil pipes are 110mm round pipe.

Can you post a pick of this pipe in-situ?

Ok that's not a soil stack, it appears to be a vent to stop the water being siphoned out of the adjacent gully trap or elsewhere.

To answer your question, it doesn't need a cowl as it's purpose is to draw air in to prevent back siphoning.

I should add that soil stack cowls are to stop birds falling in, I doubt you'd have that issue.

A soil stack is 110mm round pipe that your toilet waste feeds into. It's usually a straight vertical pipe that goes into the ground and feeds into the sewage system, the top of it extends above the eaves.

Not sure what you've got there, as standardg60 said, it must be some kind of vent for the waste system but it's not a soil stack.

Where is that going to when it goes to the gulley in the ground?

As stated already that's a gutter pipe fitting you have in your first post but could still well have been used as some sort of soil svent by some cowboy 🤠

FWIW I have no soil vents on my waste system, for the reasoning that like yours it's all on the ground floor so there are no vertical falls that would create a vacuum.

If you're not having any issues then your current setup is fine, and is a lot neater than a 110mm soil vent pipe.