Hey guys!
I was in your same position a year ago - it actually prompted me to get an account on here so I could give you some first hand experience. I am from North America, so was out of the loop on the real state of affairs. As a current student of the LSE program, I will let you know what I would have done differently - and that is attend UCL. I have friends attending the MSc in Public Policy at UCL who are getting much more out of their program in terms of employment prospects...the program coordinators work hard to set them up with employment opportunities and valuable networks as well as funding for PhD studies. This is absolutely critical due to the harsh reality of today's economy. For the LSE program, you should have an interest in management - staffing and organizational theory as well as an interest in public policy. In terms of cache, UCL is ranked amongst the top unis in the world on world rankings, time and time again, whereas LSE is often not part of that group. I hate to say it may be true that the vast number of MSc's LSE offers may just be opportunities to enhance revenue as opposed to setting students up for real success. The program is also more expensive and my UCL counterparts will have less debt (and probably much better positions after the program to top it all off). If you were studying an economics subject, LSE's name holds brand recognition and I'd say the choice is clear .....but in this field, I would say go for the UCL and do not find yourself in the same position I am in. Do not get me wrong...studying at LSE has been a good experience (and challenging!) but it is not the experience you will get at UCL. The School of Public Policy at UCL is the only one geared entirely towards graduate studies - it is THE policy school in London for post-grads.
PS!!! It goes without saying that you should choose Oxford if you get in. As you know, it is ranked even better than UCL on world rankings..and would top the other programs.