Of course I’d recommend the Sherlock Holmes stories, but he’s not on the official police force. I’ve heard good things about the Sergeant Cribb novels, but haven’t read any of them: Peter Lovesey - Wikipedia
There’s theBlackstone seriesby Derek Lambert (writing as Richard Falkirk) Blackstone’s a Bow Street Runner, more towards their end, just before the Met was established. It’s Georgian/Regency not Victorian, but sometimes do concern Victoria. There was a recent reprint.
Detective Inspector Jonathan “Jack” Whicher (1 October 1814–29 June 1881) was one of the original eight members of the newly formed Detective Branch which was established at Scotland Yard in 1842.
In 1860 he was involved in the Constance Kent murder case which was the subject of Kate Summerscale’s 2008 book The Suspicions of Mr Whicher and the film of the same name. He was one of the inspirations for Charles Dickens’s Inspector Bucket, Colin Dexter’s Inspector Morse, Wilkie Collins’s Sergeant Cuff and R. D. Wingfield’s Jack Frost, among other fictional detectives.
I was going to suggest the Thomas Pitt series. I have read most of them and they are very good. I’ve also read the William Monk series which are also very good. Set after the Crimean War. Both main characters are with the police. Everything I’ve read by Anne Perry is very good.
Are you up for non-fiction? It’s not a perfect match to what you’re looking for, but the police stories in Reprinted Pieces by Charles Dickens are fascinating. It’s just a small part of the book, but you can read it on line (dead easy to find), so that’s no particular problem.
The Detective Police
Three Detective Anecdotes
On Duty with Inspector Field
Down with the Tide
At the time there were three or four detectives in the UK. Dickens knew all of them and was basically a groupie. His non-fiction is (my opinion) far better than his fiction.
Well, Monk was with the police originally, then a private investigator, then back with the police.
I enjoyed them for a while, but continuity is poor. Runcorn’s personality changes to suit the plot, Margaret’s personality did too, and she lost a sister and gained two new ones. In one book Rathbone has his own house, and in a later one he say he could if he wanted to, but prefers to rent rooms. There was one so extreme between books I checked see if there was another edition because a guest character knew who Charlotte really was at the end of the book, and knew his daughter married because she might be pregnant, but had forgotten both of these when he showed up again and these were major plot points. Charlotte’s child briefly went back to teething in one book before reverting a 5 or so year old (been a while, and can’t recall exact age). One book says Emily redecorated the house, another says it was perfect so she never changed anything. Vespasia had a deceased daughter and 8 surviving grandchildren in one book, only to be called childless later, IIRC. The character/appearances of Charlotte’s brother-in-law is also a bit of a snarl.
I know reading them all over a few weeks instead over a decade makes me notice those more, but finally I got tired of it. Might read more Monk books, but not more Pitt ones because I don’t like what’s happened with Emily’s character lately, and especially because he does all the political crimes now, and I’m not in to politics in my mysteries. Or war-based ones. I want a murder mystery, with war and politics only giving flavor.