Most independent secondaries will offer a small number of 100% bursaries which are means tested. To qualify for the full 100% income would have to be low - some schools quote figures on website of around £16k so this could well be benefits. To qualify a child would have to pass the entrance exam and possibly to perform very well if there is a lot of competition for bursary places. Often such candidates can also qualify for help with trips and uniform too.
It's interesting, because many schools have lots of applications for bursaries, but they are mostly from the middle classes who would be hard pushed to afford the fees. Many schools don't have many applications from those whose families are fully on benefits or from low skilled backgrounds. This is because many such families don't know about the bursaries and also because people often exclude themselves by deciding that their kids wouldn't 'fit in' or 'it's not for the likes of us' - schools are very keen to genuinely widen access and not just to the middle classes whose professional salaries aren't enough for fees. Often few families on benefits apply and there are certainly more that could get bursaries because their kids could pass the exam and sometimes pass it at extremely high levels.
I think OP is trying to reach out to families on benefits and to make them aware of the possibility.
Is it very hard to be such a child? I have seen it, and I think it varies. For some children, their background experience and family is very very different to that of the majority of the Independnet school they will attend. Where values and attitudes are hugely different and especially if someone has a very disruptive family life, it can feel there is a huge gulf and children can find it hard to relate to those in the school, plus feel excluded from people at home who might see them as 'traitors'. These problems are more likely if the child has applied due to encouragement of someone outside the family and if the family don't really support the application and school and if the child feels a really strong commitment to the family and is suspicious of the school and the people within it.
I have also seen children from very modest backgrounds absolutely thrive. Often, someone in the family has had real aspiration for their child who has been highlighted as able, and has done a lot to find out about opportunities and to go through the application process. Even if the background is very different, there can be lots of support and pride in the success of the child.
Regarding other children and parents and money issues......well, I think that children are less interested in money and background than adults are, and children make friends based on who is fun to be with. In the younger years, not being well off might mean not going on some of the optional residential trips - but not everyone goes anyway. If day trips are included as part of the bursary, there shouldn't be a feeling of exclusion. When it comes to going to parties and similar, most kids or parents don't notice or care if a small gift is given, and most children are happy to go to any kind of house for a social event. Whether living in a smaller house or the less good part of town makes parents or children feel inferior is a personal thing and down to self confidence - can be an issue, but doesn't have to be. Perhaps it's easier for a well educated low income family to be confident and hold their heads high, than it is for a family from a background that feel very very different?
As kids get older and have more of an independent social life, perhaps very limited access to funds has an impact....so not having £10 to pop out for coffee or £20 for cinema and pizza might make joining in harder.
The stuff about holidays and lifestyles and cars.....some people feel small about those kind of things, but others don't and actually most well off people barely notice and don't judge or care anyway.
All that stuff about Prep parents paying for teacher presents, book days, etc etc are fortunately much more a prep-primary thing. It's often the 'newly arrived' or newly able to afford independent school people who are keen to have all new uniform and to go on every residential trip anyway, and those who have had generations of Independnet schooling who are first in the thrift shop for second hand clothes or driving an ancient car.....but again, they have the background which allows them not to bothered by flash stuff and what other people think. For those who have never had this stuff or the educational background, or the jobs and who live a very different life, it might be much easier to feel low self esteem over these things.
Bursaries can be great and they can change lives. Schools love it when someone from a disadvantaged background comes into the school, thrives in lots of activities and achieves a pile of great results and goes off to a great uni and onto a top career. It is possible, and what a great thing to offer.