Yep
The whole "rich Nigerian/Asian" stereotype is very rarely seen around LSE. Most of the people who come from African countries, in fact, have lived in the UK for most of their lives, and behave in a fairly decent ways (at least the ones that I've encountered). The overseas Asian students, meanwhile, are some of the humblest people I've met. You don't need to go to a super-wealthy private school in Singapore to get to an international university - state schools offer the same support, and most government ministries offer a number of high-paying scholarships to those who promise to return and work in their country after graduation (a similar system applies to Hong Kong). This means that, short of coming across as arrogant, most Asian students at LSE are, in fact, fairly serious academic weapons who have more or less sorted what direction they wanna take in life and make most of what London offers. You'd be surprised at how hard some of them party
In terms of halls, the only issue that I have is that certain ones are chock full of the richer internationals who are often unwilling to chat to others in general. High Holborn is often cited as a must avoid, due to the way in which you're going to have to be in contact with your flatmates a lot as a result of how the flats are structured (it's uncatered, and you share a kitchen and toilet with several others), and the fact that the only people who can afford it are fairly wealthy. My hall was superb, in that it has a large bar that many frequent, a good mix of internationals and Home/EU students, and a decent committee that put on plenty of events that gave Freshers' Week some structure.
The myth about foreigners not speaking English is just that - all of them have a capacity to speak English (remember the IELTS requirement?), and, indeed, countries such as HK and Singapore speak English as an administrative language alongside more native tongues such as Mandarin, Canton, etc. Virtually all the people I've met from these places have a high enough level of English not to impede day to day communication. The real issue can be found in the far smaller society of mainland Chinese, who have not had the same exposure to English and often appear exceedingly polite or frigid because they don't feel comfortable enough with the intricacies of it.
Regarding social cliqueing during teaching time, whether this happens in your course depends a lot on what you're studying. In A&F, which is dominated by Asian students, one may feel a bit left out, particularly considering that their majority gives them the comfort to speak in their native language in front of everyone else. My law lectures, on the other side, couldn't be farther from that. As for people only hanging out with others from their country, I've seen it happen on occasion, and many at LSE do openly acknowledge (and lambast it), but there's such a wide variety of students in societies and halls that it shouldn't be an issue. I've personally hung out with a group of friends who range from Greek to Iraqi, and I can honestly say that globalisation has made us feel more intimate with each other than one would have expected based on the cultural difference.
The main structural issues I feel are present are that a sizeable part of halls are taken by first year Master's and General Course students, who, while being perfectly good people, tend to be 2-3 years older than the freshers and often don't socialise as much in the communal areas (this is untrue for a couple of GC students I've met from the US, but they are the exception). Secondly, the large distance between halls means that you can't really go about setting up a social circle with people from other places until societies start kicking up into gear the second and third week. I've managed to avoid this with a few people I knew from different halls before I came to LSE, but your social circle will largely be limited to your accomodation at first. However, for those glorifying the collegiate systems of Oxbridge and Durham, this cannot in itself be seen as too bad a thing, considering that the popular halls cater to a minimum of 300-400 people (with Bankside, the largest, having 600+).