I really enjoy Liz Evan's "Grace Smith" series, also Stella Whitelaw's "Jordan Lacey" books.

The two series are half serious and half comic. Both protagonists are bumbling private investigators who manage to solve crimes in spite of themselves. Sort of like Stephanie Plum but a little more serious.

I'm wondering if any PBS members are aware of other British mystery authors who write similar books.

The Charlie Fox series by Zoë Sharp. A bit more serious (less humor) than the ones you've mentioned, but very good IMO.

Charlotte 'Charlie' Fox has been described as a female version of Lee Child's Jack Reacher. Like Reacher, Charlie's background is military. She was a first-class shot who was selected for Special Forces training, but that's where it all went horribly wrong. Chucked out of the army in disgrace, Charlie drifts through a variety of jobs in the early books, teaching self-defence and working nightclub doors, and house-sitting on a run-down housing estate. But then she meets up with a spectre from her army past − one of her old training instructors, Sean Meyer. Sean is now back in civvy street himself, running his own personal protection agency. He offers Charlie a job and, after a rocky start at a shady training school in Germany, she embarks on a new career as a bodyguard.

Unfortunately the earlier books in the series can be somewhat difficult to find because the series didn't get a US publisher until book 4.

M.C. Beaton's Agatha Raisin, Patricia Harwin's Catherine Penny come to mind.

I am reading Dorothy Cannell's "The Thin Woman" and find it very funny.