As an LSE and UCL alumni, I can assure you LSE and UCL are not better than Oxbridge. Statistics wise UCL may look good, but that's only because it's two times larger. Oxbridge is more influential in early all aspects, and their gaps tend to be larger in the last three or four years. The best publication is always carried out by Oxbridge presses while there is hardly anything that goes to the UCL press. In around 2005 to 2010 London unis surpass Oxbridge seems to be a real thing but now they have become increasingly less attractive to students. What you are doing will be seen as trolling and give others even worse impression to London unis no matter what your true intension is.