taff is right mate, it is flooded at the moment but the more people you can get your CV and covering letter out to the better. Some are bootneck only but there are lot out there that will recruit tri service. Be prepared to follow up emails with CV's though as you can probably imagine companies get smashed with hundreds of CV's every day. The Seamans discharge book etc, like taff says is tricky but if you look into it there are ways of getting one without having a coy sign you off.
You might also want to look into doing a Maritime Firearms Competency Course. You can google companies that run them but a lot of employers want to see that you have done one and have the certificate as shipping companies are asking for more and more paperwork!
Unfortunately mate the two companies I work for only employ bootnecks, and you have to be on the books with a company to get a letter so you can get your Seamans card and discharge book. If your in the South Wales area get in touch with Ambrey Risk, they were recruiting and take on Army and Navy lads. Get your CV out to everyone, unfortunately the market is saturated now so lots of companies have stopped taking blokes on. Im off back out in a few days so keep me updated on how you get on.