Writers' Forum has a monthly fiction competition. You can enter online, fees apply, with winners being published in the magazine as well as getting some cash. 1,000-3,000 words, enter any time.
The small press Indigo Dreams is always on the lookout for voices that match their ethos. They also publish magazines. Sarasvati is open for submissions. Free to submit, prose of up to 1,000 words.
If you are very quick you could still enter the Marple Short Story and Poetry Competitions. Short stories up to 1,700 words, £3.50 an entry.
WritersReign have a short story competition too, entries of 1,000-1,500 words, entry fee applies. They also have a really useful list of short story competitions, I haven't looked in detail yet but will be sure to.
Writers Village allows entries of up to 3,000 words in any genre. Submitting two stories costs £10. Deadline 30th June.
The Aeon Award 2011 Short Fiction Contest is worth entering if you write science fiction, fantasy or horror. The deadline is November (there are four rounds). Submissions can be up to 10,000 words which is great for people like me who rarely write anything below 1,500 words. 7 Euros to enter, c.£6.29 via Paypal.
Lastly, The Manchester Fiction Prize. Entry is more expensive than usual - £15 - but the prize of £10,000 is where the money goes. Entries of up to 3,000 words, deadline is 12th August.
If you enter - good luck!