That's definitely something that will be covered under warranty. It's really frustrating to see how often this seems to happen with G53s....I wonder if the assembling factory is just using a crappy DC jack.
Anyway, if you bought it in the U.S., you should have the
"Asus 360" international warranty coverage, as well as
"Asus ADP," one year accidental damage coverage, both with free shipping. (Note that units purchased from certain retailers, like BB and Staples, are excluded.).
They claim that they aim for 3-day turnaround on damage repair, so hopefully, you can get a quick fix at an Asus service center there in the U.K. But considering that you're only going to be there for a month, you should try to get some assurance that you'll get it back before you leave.