When people buy a house they use money to pay for it, class is not a requirement to secure a mortgage for a home.
I live in an affluent area, which makes this house seem like a total bargain… but not everyone who lives there is middle class - there are tradesmen who specialised early on in trades who earn a very good income - for example a neighbour who trained as an Air Conditioning installer, who has grown himself a fabulous business, but doesn’t meet the typical ‘middle class’ description… but has obviously been successful and worked hard to achieve all he has and lives in a much more expensive house than the one you have highlighted.