I think if any government REALLY wants to improve DCs life chances, the best policy is to encourage 'wanted' children- which is a HUGE issue!
Whilst I agree entirely with schemes that attempt to reach out to 'disaffected' youth, the simple fact is you are weeing in the wind. At its core, I believe that for a DC to have a reasonably good 'chance' in life in general, that DC MUST feel themselves to be valued, cared for, nurtured and loved. I am annoyed at how much time is now taken up in school trying to teach the sort of thing a DC OUGHT to learn at home. THIS is why our curriculum is so full of 'soft' subjects!
Of course we must continue to help these DCs as best we can- ignoring the problem only increases the risk further that they will become tomorrow's 'social problem', spawning yet further generations of the unteachable.
On the subject of the ever expanding 'good' school, I think it was BonsoirAnna who noted that the nature of a good school changes with expansion. We have seen this locally: Due to the direness and failure of a couple of comps in our nearby big city, many DCs came from there to the comp in our small market town, Within a year we had knives, drug trading, punch-ups at the school gates. And a groudswell of existing parents removing their DCs and sending them 8 miles to another town. Ridiculous.
I think one DOES reach a point where all those DCs who can be helped have been and we will always be left with a small group who will only ever disrupt classes and wreck the education of others.
We may praise grammar schools. Once upon a time, one's future was completely circumscribed by one's birth. The grammar school came along and gave the more intellectual the chance to change their futures- into the sunlit uplands of the massively expanding middle class professions. Meanwhile, jobs for the less academically able were 10 a penny, honest employment providing income, respect and status.
Now the manual jobs are disappearing like scotch mist, (and many middle class jobs are in trouble in financially straightened times) and the grammar schools have to a large extent been hijacked by the 'private-abled' parents. We live in a different world!
MY solution (apart from the nasty spectre of the social engineering necessary to ensure more babies are supported and wanted!)- is a massive expansion of selection: We'd have academic schools (or section in a school), we'd have PROPER technical schools which you'd have to have an interest and ability in to gain access; you'd have Sports colleges; Arts colleges etc. As I say, perhaps all on the same campus. But this One Size Fits All educational dog's breakfast we've been left with suits few except those parents able to engineer their DC's passage into a state grammar.
Or those who have done what we've done: gone to a lot of hassle and expense to get into the catchment of a good comp that happens to be in Middle Class Central!