Hi Tooomek,
As Student88 says, as long as you have the right to live and work in the UK, and provided your English meets the required standards (which from your post It would appear that it does), then NATS shouldn't look at you any differently to British nationals.
Obviously NATS will be making a considerable investment in you, so they might quiz you a little about your long term aspirations etc. if you are lucky enough to get through to the interview at stage 3 - they'll want to know that you intend on moving more or less permanently to the UK and won't be planning on heading back to Poland or elsewhere after only a few years.
Other than that the only thing I can imagine is likely to be any different for you to any other candidate is the security clearance, which may well take quite a bit longer and be more thorough than for British nationals.
Good luck at stage 1
