Some good recommendations.
I’m not sure you’ll find many novels about middle class people during the Regency period. At that time, the middle class was fairly small (I think). The majority of the population were either farmers/landowners, merchants, or poor, as in very poor. During the Victorian period, the middle class grew in both size and influence. If you read Henry Fielding, for example, who wrote almost exactly a hundred years before Dickens (1740s), the whole tone and feel is different. It’s a different flavour or atmosphere - more brutal, coarse, instinctive and wild. Between Fielding and Dickens you get middle-class respectability.
As for recommendations, there have been some really good ones (I second George Gissing and Arnold Bennett). Dickens doesn’t just write about the poor. (Orwell said his real subject isn’t the working class but the lower middle class.) I’d give him another try. He’s very sympathetic and broad minded, but I’ve never thought of him as a working class writer. He is solidly middle-class in his morality and outlook. Oliver Twist and Pip, for example, remain weirdly middle-class even though they grow up in poverty.
How about H G Wells? He didn’t just write science fiction. The Sherlock Holmes books are wonderful as well, and don’t just deal with crime - many of the characters are middle-class (as is Holmes himself). Oscar Wilde does write about the upper classes, but his fiction is more concerned with a particular branch of the upper class - the educated, refined, art-loving type, not the oafish, heavy drinking fox hunters. D H Lawrence might be worth a look. He is a 20th-century writer, but Sons and Lovers deals with a fairly ordinary family - not poor exactly, just ordinary. That was written around 1910 (ish) and has a Victorian feel. Or how about Madame Bovary?