This chart is taken from this article in The Conversation, and shows the proportion of children that get into grammar schools by affluence (from the least affluent on the left to the most affluent on the right).
We have long known that children on free school meals are a tiny proportion of grammar school intakes, less than 3% (according to the Sutton Trust), compared to an 18% average in the communities they are based in.
This new analysis shows, by using pupil-level data, a direct relationship between the affluence of a family and the likelihood of a child getting into a grammar school. This ranges from just 2% getting into grammar schools, for those in the bottom percentile, to 79% for those in the top percentile - in selective areas.
The researchers went on to compare the proportion that got into grammar school with results in Key Stage 2 SATs, to see if the difference could be explained by any gap in academic achievement. There remained a dramatic gap:
This may be due to the ability of the better-off to pay for tutoring to the test.
The full range is shown in this graph, showing each KS2 percentile from the least successful on the left to the most successful on the right:
Whatever effect grammar schools have, this research shows very clearly that they are a means to less social mobility, not more.