YANBU, with some caveats.
Some middle-class people are concerned about inequality because they can see that although they're personally OK, the UK is very unequal in general.
And some middle-class people are concerned about inequality because they think they are poorer than they actually are (see third link).
And some middle-class people don't care about inequality because they perceive that poorer people have it easier (e.g. all the "free" stuff they get, which is meant to even out some of the difference, but of course doesn't actually do it very well). Like that thread recently where someone was convinced a neighbour earning less than her had more disposable income (whether or not that was actually the case, and ignoring all the other differences between them!).
Obviously the benefit system is not well-designed, and there are some steep drops at certain points (my partner doesn't work more at his minimum wage job, partly because he would only keep 45% of the extra, on UC, and he'd rather have the time than the money). But there is also usually room to simplify one's lifestyle if one earns plenty but still feels poor. People tend to spend what they have available.
And even if a middle-class family did have proportionally less disposable income than a poorer family, they would still likely have more in absolute terms (and often assets such as a house).
Our household income is in the lowest decile, and we're in the precariat (lowest class) according to the BBC calculator. I complain about inequality in general, but not so much my own situation; we're mostly OK (though of course it could always be easier!).
Income percentile calculator: https://ifs.org.uk/tools_and_resources/where_do_you_fit_in
BBC modern class calculator: https://www.bbc.co.uk/news/special/2013/newsspec_5093/index.stm
Conversation article: theconversation.com/where-you-think-you-are-in-society-not-where-you-actually-are-matters-for-how-you-think-about-inequality-259715