A very comparable writer (to Meg Elizabeth Atkins) is Marjorie Eccles though her Gil Mayo series is now long-established – 13 books to date, though the last was in 2001 so I suppose it may have stopped now.
The particular books I read were Late of this Parish and Killing Me Softly.
I suppose ‘cozy police procedural’ would do as well here (all depending
on your definition of cozy of course!). From my point of view
‘sociological suspense’ does better especially for Eccles –
and she is rather better at the social observation, where Atkins
is rather better at characterisation – though this conclusion
is based on very limited evidence! Late of This Parish has
a school/church background and is more of a traditional
mystery than Killing me Softly which may form part of a
general series progression?

As with Atkins I would recommend Eccles to anyone looking for
a good, solid, middle-of-the-road, Britmyst. But to borrow from the
library rather than buy (well unless you are rich of course!:)).

(June 2007)