It is certainly believed that the London School of Economics (LSE) are rather infamous on their GCSE policy in UCAS applications and require the 'best of the best', well this is certainly the majority opinion of online student forum (the student room) any way.
There does certainly appear to be evidence behind this claim though.
A statement by the Economics department (found on the LSE homepage) regarding frequently asked questions on Admission criteria.
"students have already achieved excellent GCSE grades including the majority at A and A*. The Economics selectors consider not just the number of top GCSE grades that you have, but also your overall GCSE subject profile."
Then I found a similar statement by the Geography department again regarding the same issue, but instead of the word 'majority' they have inserted 'significant' which to me might indicate (with further research around the student forum) that the weighting that LSE put on GCSEs aren't equal throughout their departments.
If you have done your GCSEs it is more than likely too late to alter your GCSE subject profile, but if you are choosing and bearing LSE in mind I would do some more research into the stronger combinations of subjects that LSE is preferring - probably try to stick down to the more traditional subjects.
Even though LSE is a competitive (one of the most oversubscribed in the country) university to get into, but even with LSE there are more competitive courses than others for example Economics is considered one of their most competitive courses.
However here GCSEs will have may have more weighting due to such a large proportion of candidates applying with the top grades at A levels, it is needed to further differentiate candidates, rather than a less competitive course at LSE.
(Therefore LSE are kind of forced to place a high regard on GCSEs as really they are limited by the things that they can differentiate a candidate on).
So it might be worth asking yourself also how competitive is the course at LSE I am applying for (more on this later on).
If you go on the student forum site you will find numerous statements saying things such as needing a minimum of 9A*s to apply to LSE for Economics and so on. These should be ignored (there are a whole host of candidates that break that particular rule that is for sure), but these are the kind of norm candidates who do get offers to study at the LSE.
However, what I want to stress in this article is that, although LSE do place a high regard on GCSEs, that isn't the only factor they use to distinguish applicants. For example, they also state that they place particular emphasis on the quality of your personal statement due to them not interviewing candidates.
But yet again, obviously the better your GCSEs, the better your chance of an offer.
(So you might have just below the average on the GCSE (e.g. 2A* and 8A for Economics) front for LSE, but you might have come up with one of the best Economics personal statements on offer, you don't know how much weighting they will place on it and so they might then give you the offer.)
Instead you could consider are your GCSEs realistic, are they actually mostly made up of A*'s and A's? If they are then that is great, maybe you should apply, what do really have to lose? Just make sure you make your UCAS application that it is the best that it can be.
(If you are still unsure on the stance of your GCSEs, maybe try a post in the student room, to get a feel of the kind of applications that are applying for your course at LSE, don't use LSE as a whole as it will vary, bear in mind most of them are students as well, so don't take their word for gospel).
But wouldn't you rather use that one in five options on a university you really want to go to with a small chance of getting in, and not have to regret not applying, rather than applying to a university you don't really want to go to with a high chance of getting in, and regret not applying to LSE.
I know which option I would choose.