I think that this may be a case of post hoc ergo propter hoc.
Highgate obviously has its own junior department, and most of those children go into the senior school at 11 though even then they have to meet a minimum standard first to get into the junior department from the infants and then to get into the senior school. Most parents who want Highgate as a senior school will try to get into the junior.
There are then a further 40 odd places at 11+, and applications for those is based on the entrance exams together with interviews - there are 2 interviews, one where the child is in a pair or trio, and one individual interview. Highgate are looking for a certain type of child and they are specifically looking at how the children interact and behave towards each other.
In reality whilst there will be admissions from state schools to these schools, property prices and tiny or selective (by religion) catchments can mean that a state primary school doesn't have such a significantly different socio-economic mix that the prep schools. If anything many London prep schools are full of immigrant and expat families who either could not or chose not to play the state school selection by postcode/faith game, and are certainly ethnically far more diverse than their state neighbours.
So it doesn't surprise me that a couple of CofE schools may have been successful in getting entry in years past. But the fact that the pupils were at those schools will not have had the slightest impact on their entry to Highgate. They had to pass the entrance exam and the interview.
In terms of admissions to private schools, I can't speak for the whole of London but locally the co-eds and boys schools were inundated with applications. The number of children born in London is on the rise (approx 100k per year in 2000 and 2001, the current year 6 birth years, rising to about 130k currently), so even despite the economic outlook there will be plenty of competition for the good private schools for some years. The position is likely to be quite different in some areas outside of London though.