My DC go to a school like that. I've even heard the "where children go if their parents are not bothered about their education". The person who told me this then visited the school and ended up putting it down as their first choice. :o
The children base their friendships on who wants to play chase in the playground, or who can make the most mess in the water tray. They really don't care whether the other children live in a bedsit or a mansion.
The staff are used to dealing with all kinds of different backgrounds and needs, so the pastoral care is fantastic. The children themselves are also very accepting of each other's differences. It's very much like a small community.
My DD was shocked when she heard that her cousin had been bullied at her (church) school because she had a different accent to the other children in her class. At DD's school, many of the children are bilingual and no one pays any attention to accents.
The school does a lot of work on inspiring children to achieve more and try out new experiences. They do this through trips, visitors, workshops, and as part of the class topics.
A lot of the families start off there because there were no places elsewhere. Many choose to stay even when their preferred school later has a place for them.