This won't be based on observations that show that children from all areas have equal chances when it comes to language based performance. The truth is there are huge differences which cannot be explained merely in terms of inborn SN.
And language based performance makes all the difference when it comes to chances in later life.
Whether a leaflet will make a difference or not is a different matter. But I don't think anyone can doubt there is a genuine problem.
What I have found with some friends is that they do talk a lot to their babies: pointing out butterflies and counting fingers.
But then as their children reach school age and even more so junior school age, they don't go on to the next stage which is conversation. Discussing things, asking for the child's opinion, telling them about their adult experience.
And while this is not essential for learning to speak in the first place (babies do learn to speak even in cultures where nobody ever addresses a baby), it probably is essential for the kind of high level linguistic performance that is expected for most reasonably well paid jobs these days.
The reason middle class children have better chances of getting into a good university or a well paid job is a thing apart from the relatively small number of children from all classes who have actual speech defects.
It may well be that the current government are trying a diversion technique for nefarious reasons of their own. But the problem is one that has been recognised by all governments for a long, long time. Similar information was handed out when my children were little, under a Labour government.