Comparing the overall reputation of universities when you want to do a particular course is about as useful as comparing National GDPs when all you want is a nice beach.
I take real issue with the notion that "it's always been:Oxbridge 1st and 2nd. With imperial and lse battling it out for 3rd and 4th respectively. UCL lags behind."
There is very little objective evidence to back this up. Further putting imperial into the equation muddies the water. Imperial is a science university - how can it possibly be compared to UCL's other departments? Why should a law student care whether its university can cure erectile dysfunction?
LSEs international reputation is one based around its social policy courses; not its law course. As I have said previously, if your metric is getting a job in law, then LSE offers nothing over UCL.
It only seems to be those at LSE that claim 3rd place... few others would agree.