I was in a similar position but for history and politics. It would have been a non issue for me if it weren't for my school raving about presteige as I much preferred Warwick to LSE, both in terms of the environment and the course itself. My school generally talked about Oxbridge, LSE, Imperial and UCL having this unmatchable presteige, generally citing international rankings to support what they were saying. This worried me and I did a fair bit of research to try and weigh up the pros and cons of the two universities from which I was going to make one my firm and from the things I found out there isn't any significant difference in graduate prospects between the two with both being targeted by a lot of major banks and businesses. I actually know a couple of postgrads at LSE now, one of whom was an undergrad there as well, and another student who is currently in the second year of her international relations course and the general feeling I got from them was the same as the one frequently voiced on this forum: the teaching quality at undergrad level could be better and they often feel ignored by academic staff. Whilst I don't know anyone at Warwick, the general feedback around here and from other sources was that the focus on undergraduate teaching was very positive indeed. The prestiege issue is pretty stupid as well; LSE has a better international reputation no doubt, this comes as a result of it's longevity and single faculty focus which attracts a lot of top academics to the place. But Warwick, in just 40 years, has come to be regarded frequently within the top 5 universities in the country and often the top 3/4 multifaculty universities nationally. Internationally it's reputation is fast growing but still has some way to go. To secure the research funding it has (research commonly being the way by which international tables are done) in the time it has existed is very impressive and it hardly does badly as it is, coming in the top 70 frequently.
The other aspect that worried me about LSE was the social life. Whilst this may seem a little odd with it being slap bang in the middle of London, anecdotes from the undergraduate I know compounded again by some posts on here suggest that the undergraduate student body isn't very cohesive at all at LSE with a lot of people being fairly insular commonly because of language barriers (with some 50% of students being from abroad) and many people also having a very very strong work ethic that meant they were unwilling to socialise. The girl I know ended up spending a lot of time at UCL with friends she made through some old school mates she had there. I don't think this held her back this much, but she seemed to indicate it was inconvienient and she often found herself isolated within the LSE halls. If you choose LSE , I'd suggest intercolligate halls therefore. Warwick, whilst it's never going to be able to offer the range of social activities on tap that London can, seemed to provide a much more friendly and cohesive group of people. There are ample facilities onsite and beyond that there is Coventry near by and Birmingham near enough to get a train.
I placed Warwick as my firm in the end and I'm not going to regret it at all. If I decide to do a postgrad I'll consider LSE no doubt but for undergrad I kind of regret even putting it as a choice, Durham would have been a better back up for me.