I thought you may have just used the transcript on Freebmd or Ancestry and not checked the original image to see if there had been a transcript error.
I looked on Ancestry and the transcript there is as you say and Freebmd will be the same as that is what Ancestry use.
So I checked the images on Ancestry and there is something wrong with their image files. They are missing some pages so if the record office are using ancestry images they will not find her. Possibly the GRO have lost some files.
Images of Deaths in Ancestry
Image 125, Page 166 WILLIS to WILLOUGHBY
Image 126 Willoughby to WILLS
Image 127, Page 167 WILLS to WILMER
Image 128 WILMET to WILSON Agnes
Image 129 Page 174 WILSON Female to WIMPENNY
They are missing pages 168 to 173 and the reverse of those pages and so have left out most of the WILSON entries.
Then I checked the images via Freebmd and she is there as you can see on the attachment. I suggest you call the GRO and explain.