While hunting down good reading websites for my day job I found that the nice people at the booktrust have a very useful list of UK writing competitions.
http://www.booktrust.org.uk/books-and-reading/short-stories/prizes/
The rest of the site is also worth exploring. There is a writing section with author interviews, advice, and of course the above mentioned competition list. Most of the site is dedicated to reading, so have a look if you’re interested in reading suggestions, book news etc.