Each department at LSE has a huge amount of independence. I'm split between the government and philosophy departments, and they are both quite good. I've been at LSE for 4 years now (undergrad and masters) so I feel more confident talking about this.
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One crucial thing to keep in mind when looking at student satisfaction / experience ratings is the London effect. Kings and UCL are both on a par or just slightly above LSE on the rating scale. The only university in London with a significantly higher satisfaction rating is Imperial College.
Imperial is unique because of its location and very healthy funding situation. All credit to them for prioritising the student experience, too.
The jury is out as to why students in London are so much more dissatisfied overall - it's certainly not LSE specific. IMO it's the lack of space, money and time = low quality of life. My life revolves around London, not LSE. I've recently been writing a paper every 1.5 weeks + 15 hours of part time work + 20-30 hours of grad job applications + 7 hours of seminars. This city pushes you to work hard because the opportunities are so much more tangible.