The truth is, there are very few ways around this, and if you have someone that gets rejected, the opportunity that you will get him anytime soon is very slim. Mostly, players in regions that aren't considered part of the European Union have a difficult time getting into the Premier League, unless they have proven to be great footballer through reputation (either by playing for a world class club, or more often, being a staple for their international squad over many years). It's true for the UK for most employment. I, for one, have had several companies in England and Scotland that have been interested in employing me, as I have a good reputation and a lot of experience in a growth industry with a need for people wit experience, but my opportunities have been foiled up to this point because of the fact that I am from the United States.
In this year's version of the game, there is a way around it, if you have Steam. If you go to the Front Page of the game, there is a selection called "Downloads". This takes you to the in-game Steam store. There is a FMC Unlockable there called "No Work Permits", which offers you the option to abolish the need for work permits for a small price (in real money). You can also unlock this in-game by showing a commitment to developing home-grown talent in one of your saves, although I'm not sure exactly how you prove that. Be aware however, that this unlockable will only be allowed for use in an FM Classic game save.