From your PC:
1. Register a UK hotmail account at http://www.windowslive.co.uk/hotmail.aspx
2. You'll need a postal code to do this, so use "W11 2BQ".
From your Xbox 360:
3. Log out of your regular LIVE profile and sign up for a new Xbox LIVE membership using the UK email account that you just created. (You can just use your current telephone number for this part. But I just entered 123456789 for this part.)
4. Decline the offer for a Gold membership. Do NOT use a free month of gold if you have one: This content is now free for Silver members.
5. Go to the Game Marketplace > Browse > B > Batman: Arkham Asylum > Prey in the Darkness. Download it.
6. Log out of the UK profile and log back in to your regular profile.
7. Enjoy the DLC. =)
This information is extremely useful for those of us outside of Europe who want to download the Second Map Pack, "Prey in the Darkness." I tested the method. It works great. I've also refined the instructions so there won't be any questions as to how to do what.
Credit goes to Reaper98
for originally posting the method.
And if you're curious as to why this is in it's own thread: It's because the thread it was originally in doesn't really tell you that this is there in the title. It's also quickly disappearing into message board obscurity.