At least they are trying and it seems for the moment PP children are getting places at grammars where they wouldn't have qualified previously.
Govt funding has been changed so that schools with more PP pupils get more funding and those with few have suffered quite harsh funding cuts. That's certainly going to drive schools to increase the number of PP pupils on their books. My son's grammar school's published accounts clearly show a reduction in government funding which has meant redundancies and some subjects no longer being taught.
It's a fine line. You can't start accepting children who aren't going to fit in, either in terms of discipline, ability, etc. as it's unfair to other children, they don't want to risk lowering their exam results statistics, and more importantly, it's a great disservice to the PP child themselves if they're not going to be happy there and aren't going to be able to keep up with the work.
But, at the end of the day, the grammar takes the top x number of applicants, so plenty of kids will achieve a "pass" mark but not be offered a place because others have scored higher marks (or live closer). So there is scope for tweaking the admission criteria to give a modest weighting for PP children who "pass" but are too low down the list to be offered a place, and put them up the list to give them a place, but inevitably that means someone who got a higher score or lives further away, losing their place. What isn't acceptable is admitting PP kids who get low marks in the 11+ just in order to secure govt funding and tick boxes.
But, none of that deals with the "poverty of aspiration" where the parents of some children don't value education, or, as discussed on this thread, are against grammars. If the kids aren't put in for the 11+ or are entered but get no parental support with practising and exam technique, etc., they'll not get a place even with some kind of weighting.
Our son's grammar work with local primary schools to try to solve this issue. They have a scheme where the primary schools select a small number of children who they've identified may be suitable for grammar, and they go to the grammar one afternoon per week for several weeks to experience it - they have a separate classroom, dedicated teacher and support staff, etc. The aim being to get the children to want to go there themselves, so as to substitute the parental push that is lacking. Unfortunately, it falls down because it's up to the primary to choose the children to attend, and, inevitably, that means nepotism and bias comes into play - the kids chosen by our primary were the children of the staff and governors. In the end, 9 children went to one of the two grammars, very few of whom had attended the grammar's programme, in fact most of the ones who went didn't even enter for the 11+. So it wasn't a great success, but more the fault of the primary rather than the grammar!