One of the biggest organisations doing such work is the Mission Aviation Fellowship. The minimum entry requirement is a CPL and 500 hours including 300 hours PIC.
Plus references from your church and Bible training. If you are a committed Christian (which I am not), it looks like fabulous life and something I would love to do (
http://www.maf-uk.org/ ).
However, there are other jobs to be had but the details are sketchy. It seems that most pilots need to just travel over on spec, mill around finding a way to feed themselves until they come across somebody hiring. Most don't advertise. For the committed wannabe ATPLs mainly I think.
AndyRR,
Sounds quite odd but I totally agree with you. Flight Sim simply can't complete with the issues and emergencies that a comfy chair and a quiet room can generate.