Hey DGStein,
I'm a post-grad at the LSE, and also lived in the US a long time (including for my undergrad). LSE has one of the world's best IR programs, and my friends in the program seem to be quite satisfied. If you are interested in the LSE, I'd suggest you apply in before December 05 for Fall 06 start. The course tends to close soon after.
They seem to look at a mixture of things- GPA is quite important (most of my American course mates have 3.7+), and very strong recommendations seem to also be up there. The application is quite short.
Though maybe 30% (rough estimate) of the applicants seem to come straight out of UG, it seems if this is the case, make your reccomendations/statement very strong. There's the general impression that you can still get in with a 3.5 GPA if you have some kickass work experience, but otherwise you better have a pretty strong case for why you want to start a MSc straight after UG.
I know you didn't ask this question, but I'd really advise you to consider whether it's a good idea coming to a master's program straight out of UG. My coursemates w/no work experience, always say they feel their understanding isn't as grounded/complex because they lack real world training. I personally worked 3 years in 3 different countries before starting with my Masters, and I doubt I would have gotten as much out of it other wise (ie in knowing exactly what my passion was/what questions I wanted to explore etc)
Hope this was helpful!