This is one of the situations where words do not suffice.  Posterization in the corners???
In order to help and to answer, I need one of the offending images.
If too large to email, you can use the free file transfer on line system called WE TRANSFER
https://www.wetransfer.com/
My email address is wathree.ssz@verizon.net

I will flip it to Mike in a second for scrutiny
Did you try turning off SC in refine?
Fred

I must be doing something wrong. I click on the ARW  file and I get a website
 http://www.erg.kcl.ac.uk/downloads/Policy_Reports/ (the ARW file)...

Sorry.
There's one arw file dated 8-19

Fred

OK got it/

The image is full of Chroma noise!

Open in the editor, Click on ULTRA, then select Chroma from the drop down, and Poof! All cleaned up.

143 and 1144 are magnified
Fred

Hi David,
I did and had a different approach.
Your camera has a small sensor so more prone to noise in images. Also the dark corners in the sky are due to lens vignetting at that focal length, nothing to do with QU.
I started with raw preferences and for your camera set the Noise Reduction slider to near maximum so 100 iso was included. I then saved that setting for your camera by making sure the thumbnail was selected at the same time.
The blue sky in that image was nothing like a normal UK sky (I live in Rugby) so in raw refine I did a custom white balance using the upper part of the central cloud (catching the direct sunlight). This made the sky more true to life and pepped up the field colours.
In the editor I could see sky noise levels were better and to improve them further used TTS from the sky, near a corner. TTS/DFS values were -100%, 4 radius and Tone + set. This softens the blue and sharpens the cornfield area - you may prefer a lower radius. An additional improvement can be made using Ultra NR where the "low" setting is adequate.
Finally, I would crop off the top part of the sky to remove the lens vignetting     This last step will probably avoid the Ultra NR being used.
See attached below, my version and original.

Thanks Terry - yes, that does improve matters a lot. I know there is some vignetting, but the other two RAW converters do a much better job of controlling it. Having said that, this photo was one of very few troublesome ones and I was interested to see what Qimage could do; and how to approach editing it. Many thanks for you time and suggestions - it has helped a lot.

All the best

David

Well, I'm still learning about QU after all these years  I was aware of the red rectangle but rarely used it; blue or magenta get used most.
I tried this on David's image and and used levels in the editor to pep up the contrast. The histogram was concentrated in the middle of the scale so adjusting to bottom end to just meet the curve and the top end to clip a little produced a nice contrast. The overall result had reduced noise (virtually none) and disguised vignetting. 
Terry