Certainly the idea that one can leave the military and stroll into a civvy job of your choosing is long dead. That said, there are jobs out there but as FFP says above, it's a very competitive market and your 2000hrs of bombing jerry is up against similarly aged guys and girls with 3500hrs civvy hours and type ratings. The market is flat and companies recruit sporadically; it's 'just' a case of timing things right and being in the right place at the right time.
Given how flooded the market is with pilots at the moment you have to make sure your CV stands out. You only have to look through the threads on here to see innumerable people crying their eyes out about how they were rejected by airline X when they have x thousand hours and a type rating. It's all in the CV. There has to be something to make yours stand out from the crowd and some military experience (including leadership & management experience, not just flying) can help do that.
I left at the same time as FFP above and he and I both now know there are absolutely no certainties in this business. The big airline that he originally passed selection for knocked me back at the application stage, a stage I assumed I would breeze through given my hours, experience and all round fabulousness. I have subsequently though had a couple of flashes of extreme good fortune based on being in the right place at the right time and on buffing up my CV and cover letter......
Military experience does count for something but it's not the be all and end all. I've been pleasantly surprised by civvy aviation and have flown with a lot of talented, capable and decent folk; it's these sort of people you're up against.
Keep an eye on the Jet2 website. There might be some non-TR recruiting later depending on how their numbers crunch out.
PS. FFP - biff? Moi?