In reply to Dave Garnett:
> I generally rely on TobyA to put me right.
You sweety.
Come September I'm going to be teaching Religious Studies (but it seems of the A level syllabus it's mainly just Philosophy I'm teaching) and Sociology so I'm swotting up on them this summer and some international relations stuff will slide as a result, but for Dervey, I think Andrews suggestion of the Economist is a good - I don't read the finance and business sections, just the news but it really covers places that rarely get mentioned elsewhere. If you can afford to buy it weekly (I now just have the E-versions as reading it on my phone is actually much easier than carrying the paper version around with you, which I did for years.
My top tip would be start listening to podcasts - you can get on with all of life's boring tasks whilst doing some "background reading" (ok, so listening really). World Service obviously has a more international perspective than domestic BBC radio
http://www.bbc.co.uk/programmes/p02nq0lx/episodes/downloads although there are plenty of good Radio 4 programmes to podcast -
http://www.bbc.co.uk/programmes/b006qjlq Another really good one from the ABC in Australia is
http://www.abc.net.au/radionational/programs/rearvision/ It's a bit random what they focus on, but in a good way. Then they really focus on that issue and give time for real experts to explain the background, nuance etc. I'm interested in American politics so listen to quite a lot of podcasts from the US. They tend to be rather US focused of course, but that's fine as that's international news to me! This one is quite fun
http://www.slate.com/articles/podcasts/gabfest.html (but I've listened for a decade or so now I guess, so its a bit like listening to old mates argue in the pub). This from NPR is good round up every friday of some decent journalists discussing the big US and then international news stories each week
http://thedianerehmshow.org/topic/friday-news-roundup
I subscribe to all those show via itunes though, so it just downloads a new edition of each podcast whenever it comes available. It all starts of as a random jigsaw but as you understand more you suddenly start seeing how what is happening in one country is connected or impacting on what is happening in another.
Regardless of what you think of it, being British it is well worth reading some introductory stuff on the EU - why and how it started, how it actually works, what it does etc. The UK media really doesn't cover it very well but its really important to how Britain acts in the world more widely.
Good luck!