Here's the quote from the Tory manifesto about bringing back grammar schools:
We will lift the ban on the establishment of selective schools, subject to conditions, such as allowing pupils to join at other ages as well as eleven. Contrary to what some people allege, social research shows that slightly more children from ordinary, working class families attend selective schools as a percentage of the school intake compared to non- selective schools. While the attainment gap between rich and poor pupils stands at 25 per cent across the country, at selective schools it falls to almost zero.
Let's break this down:
Yes, slightly more children from 'ordinary working class families' get into selective schools as a percentage of intake. 36% compared to 35%. However this is because they've excluded anyone who has claimed FSM in the last 6 years from their definition of 'ordinary working families', which is a shocking omission.
If you include families who have claimed FSM in the last 6 years, but aren't currently claiming, then we have 52% of children in non-selective schools being from 'ordinary working families', but only 42% in grammar schools.
Secondly, yes, the attainment gap between rich and poor is much lower at grammars than at non-selective schools, however, poor kids overwhelmingly don't get into grammars. There is a sleight of hand going on here. They've said that ordinary working families are well-represented in grammars (only if you twist the definition of ordinary working family) and then they've followed that up with a comment about poor children, leading an unsuspecting reader to think that lots of poor children benefit from grammars, where in the main, they don't.
Apart from that, allowing children to enter grammars at an age other than 11 seems to be an admission that the 11+ is a load of rubbish as a selection tool. That wouldn't happen anyway because it would be an adminstrative nightmare.