Sakura - those women you speak of come from times and places where free and plentiful contraception and education about sex and pregnancy did/does not exist. I really don't think there is any reason to apply those circumstances to all but a handful of women in the UK today. The better equipped we become to avoid unplanned and/or unwanted pregnancies, the more we seem to get. 
And I am only talking about the UK - what goes on in other countries is not what we are discussing here.
You are SO wrong to say that all that's needed is 'education, good and equal education for all'. Do you think our state education is all crap then? Do only public schoolboys get 'good' education? Or do you think the state operates a deliberate two-tier system where all the ineffective teachers and lacklustre teaching methods and poor resources are channelled directly into schools especially reserved for children from disadvantaged homes? Are you suggesting poor kids are held down on purpose by the system, or what?
Do you think that schools with a history of low GCSE attainment are full of crap teachers trashing the chances of poor but clever pupils who are all deeply committed to education, and highly ambitious?
There will always be a percentage of kids who don't care, and can't be bothered. There will always be a percentage of kids with low intellectual ability. There will always be a percentage of kids who want to commit to education, but for whatever reason they are handicapped by dysfunctional home lives. They come from all walks of life, rich and poor. But let's face it - mostly poor.
The problems start with the environments they are born into, not with the fact that their opportunities in education are not 'equal'. Why it should be the school's sole responsibility to turn these children's lives around, God only knows, but they do try - they try VERY hard. But significant leaps forward with disadvantaged children will do little to dent the league tables, and if a school has lots of those children it will forever be fire-fighting, and perceived as a 'bad' school - avoided by the middle classes.
Taking private education out of the equation, all children do have access to equal education in the UK. The only exception is in grammar schools(I'm not a fan, but that's another story for another day.)
Why do we always tend to assume that apathy is a working class trait where education is concerned? No-one worries about the child whose parents may be reasonably affluent but apathetic, and there are plenty of those too.
There is absolutely no point in getting bogged down with arguments about schools in middle-class areas being 'better' than schools in areas of high deprivation. If there is huge disparity in the outcomes for the children it will almost certainly correlate to the socio-demographic intake of the pupils. Universities know this, and have been weighting their offer conditions for years, to reflect this.
My son's friend who is an exceptionally clever and highly conscientious state school (non-grammar) pupil told me he wouldn't want to apply to Oxbridge or Durham or Exeter, because he would feel 'out of place' and wanted to be around 'normal' people. That is not the fault of the universities - they are practically trying to drag high-attaining state school kids off the street! That is to do with his pre-conceptions.
If only it were as simple as 'equal education for all'. Plenty of children from disadvantaged families fail to thrive in perfectly good state education because of chaotic home environments, an inherited lack of enthusiasm about education, and a suspicion/dislike of authority, discipline, and adherance to routine.
But again, this comes down to 'what is disadvantage?' As many on this thread have pointed out, they had very little money growing up, but were enriched by parents who valued and encouraged learning, and gave them a stable, supportive environment in which to learn.
Standardising the quality of state education is not only virtually impossible to do, but it's of little use to a child whose mother can't even get out of bed in time to get him there.
I am perfectly aware that things cannot be turned around in one generation, or even two, but if we don't start insisting that young people work towards becoming at least a bit self-sufficient before we fund them to start families, and if we do not set limits on the amount of children per adult that the state will wholly or partially support, then the cycle of poverty (intellectual or financial - take your pick) can never be broken. It is an unpleasant, uncomfortable truth that no-one wants to admit, because there are no easy, palatable solutions.