Hey Paul, there are a few of these knocking about (although always room for more!). A couple worth checking out to give you an idea of what's already out there:
Cryptails: new horror short story weekly contest
Fifty word story contest: week 17!
I know there are more in the contest section, although like I said, always room for another. Plenty of writers here and plenty of space!
Thank you for the links, I was surprised not finding any writing contest to be honest.
I just submitted an entry for the fifty words contest thanks to you!