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After searching for "TV show with rat puppets," I found Roland Rat. There was apparently a spinoff series called Tales of the Rodent Sherlock Holmes. Is this it? http://www.curiousbritishtelly.co.uk/2015/02/tales-of-rodent-sherlock-holmes.html
Amazingly, after searching for years, I thought I'd have another go at Googling it, and I found it: The Adventures of Grady Greenspace! Thank for your suggestion, though :-)
I was about to respond to this (I have similar memories, but I could remember the title).
Thanks for confirming I'm not insane, though (I only really remember the title theme and not much about the content of the show itself).
TV Tropes's No. 1 bread themed lesbian. she/her, fae/faer
I have this memory of a children's TV programme that was broadcast in the UK early 90s (although the characters speak with an American accent). The tone is sort of L.A. Confidential / mystery / crime / thriller and the characters are all rodents. It's live action puppets (like Jim Henson). The theme music has a line that sounds something like "Akeela's just a rat" and a clip of the antagonist, Akeela (or whatever the name is) is shown in the background.