I'm just on the edge of this (have a dc in Y5 an ind school in London) and think it may be a combination of several things:
If you are moving into this 'zone' (ie 11+ applications for independent schools) I think it always looks worse/harder etc. I don't think anyone has ever said "thank god I'm in this position, there is so much less competition than last year"
Private schooling seems to have held up v well in the face of the recression. I'm not sure if it is because everyone is ultra wealthy in London, or more because private schooling is the last thing to go. My DC's head (London prep) told me that they have seen v little fall out at all, although what they did sometimes see as a trend - and this was just an observation, they don't pry, obviously - was fees being paid by different people, she surmised grandparents, godparents etc. So that "pool" is not diminishing in the recession as you would intuitively think it might be. The pool could be being swelled by the number of people refocussing from boarding to day. In my area, if you looked across the wide range of options available then the London day schools are probably the "better" choice anyway, and harder to get into, so I'm not sure I agree that people are "downgrading" to day schools.
Unfortunately, and again I'm speaking for my specific area, the state schools do not seem to be getting any better. So I don't think you are getting people thinking, well we'll drop out of an independent primary into a state secondary. The continuing trend seems to be state primary to private secondary.
I thought that late 2000 was a boom year, numbers wise. My nephew is in that cohort and my SIL reports that they have been caught out at every level - from unable to get into tumbletots onwards. i suspect that is a large part of it.