oh thanks for that inf, funnyperson - it does sound very attractive. If DS gets an offer from LSE it'll be something to think about.
Still keeping fingers crossed for your DD here 
Fewer overseas applicants are successful then UK ones. There is a long & complicated pdf document on the ox website with admissions statistics from 2009 (I assume 2010's haven't been worked out yet) - \link{http://www.ox.ac.uk/admissions/undergraduate_courses/how_to_apply/admissions_statistics/\link on this page}
p7 gives annual figures for "all domiciles" averaged over 2007-2009:
state schools: 6405 applied, 1502 accepted - 23.4%
independent schools: 4671 applied, 1361 accepted - 29.1%
others (not just overseas but including them): 3025 applied, 315 accepted - 10.4%
The same page gives those stats by course too.
p6 breaks the figures down by course & gender, 2009 only
p8 shows percentage interviewed by course, average of 2007-2009 again
(I've been poring again, can you tell?
)
The breakdown of acceptance rates by subject/type of school is v interesting - there's a huge variation, eg
Economics & Management 12.6% state, 12.7% independent
English & Modern Languages 15.4% state, 26.0% independent
History & English 11.3% state, 9.5% independent
European & Mid Eastern Languages 45.5% state, 16.2% independent!
(total numbers mostly pretty small but still...)