My eldest daughter, who has just completed her first year at university, went to a girls grammar school. She herself came from a state primary.
JohnFarley's point that grammar schools tend to be in better off (financially) areas is a fair one, but it is important to remember too that they quite often no longer operate on any form of "catchment area" basis. My daughter's school was a good 20 miles away from us. That said, I wouldn't actually say it was in a wealthy area. It was in a normal residential area with a mix of privately owned and local authority housing around it. It was adjacent to a council estate too.
Children can come from far and wide to take the 11+, so many who do get places do not live locally to the school and it matters less these days where the grammar is actually situated as long as it is well enough served for transport links.
With regard to size of family income, our experience of having a child at grammar school indicated that it had a much higher than average number of students from relatively wealthy backgrounds. Whilst a fair number did come from state primary schools, a fairly sizeable proportion had been privately educated up until they got their place at the grammar.
We were not one of its better off families. It was hard sometimes. You could tell from the demands the school made that it was (and remains) fairly used to families for whom money is no problem, thus not having a level playing field for the rest of us who might struggle to meet some of the costs at times. I am not in any way wishing to be discriminatory there. I am just stating the way things were.
I also have two younger daughters who have not gone to grammar. They are at the local catchment area comprehensive, which has been making great strides forward academically and in other ways over the last few years and has now completely turned itself around from what it used to be. Financially, it is easier for us too. Obviously it does have a mix of well off, average and poorer families, as well as children from a wider variety of differing backgrounds. For those of us on fairly limited budgets it is much more of a level playing field, more understanding and much less "in-your-face" with its requests for money.
I know this post has come out quite long. It is just my perspective, as a parent of limited financial means who has put children through both types of school.