Here's some empirical evidence from my experience - having done three very late applications in the past which all ended with success.
According to my past experience. No problem applying late - even the last hour.
Jobs 2013: I have made last hour applications for two job posts recently, one for Computational Biologist at ICL and one for Bioinformatician at ICL. Both led to interviews followed by acceptance. Remarkably, the Computational Biologist post stated that "it is essential that the post holder has a PhD", which I did not have! I have now started this job.
MSc Course 2012: I was the last applicant of the Bioinformatics and Theoretical Systems MSc with CISBIO - most people applied during their BSc e.g. many on the course applied February but I applied in October after finishing my BSc! Not only was I accepted, but I got a scholarship that I did not even apply for! In the interview panel was a chair of BBSRC research grant, who set me up with the scholarship after the interview.