To make a rather broad generalization, many urban fantasy series tend to feature protagonists that seem to be either from the wrong sides of the tracks with a dark history, borderline con men, or they belong to some sort of barely mentioned supernatural crime fighting group that operates in secret within the bowels of a real world police force. American authors tend to lean more towards the former, while British authors lean to the latter.
Peter Grant is the main protagonist in Ben Aaronovitch’s series. He’s a London cop training to be a wizard. Midnight Riot is the first book in the series, and I have a review with some SPOILERS after the cut.