Writing Magazine run monthly competitions on various themes throughout the year. They also have subscriber-only competitions. More info
I came across this in Writers’ Forum magazine (Dec 2018). A novel-writing competition, sponsored by Your Cat magazine. The first prize is a three-book deal. The genres can be romance, fantasy, historical, thriller or a Christmas story! But get this, there has to be a cat in your story! Yes, you have read right, be sure your novel features a feline to qualify for the competition!
The competition is open to new writers only (unpublished), however your manuscript must be assessed by an editorial service first.
Short Story Competition run by Costa, deadline 1 August 2019.
Sharon's Writers Tidbits 
Hello Sharon,
How can I send you information about our competition to add to this page?
https://www.benchtheatre.org.uk/supernova.php
Many thanks,
Robin