Not having an ATPL (ie: unfrozen) was a real pain in the butt when I applied for Brits. Even though I had some jet time none of the airlines would send me a form because I didn't have a full ATPL.
I was given a chance after attending a BALPA job conf with 1200 hours. After being offered the job (all very last minute in true airline style) there were two guys on my course with 200 hours so if they turn you down it is not necessarily because of your time.
Stay tuned: with recent recent moves in the job market, recruitment chances can only get better! Good Luck.