I concur with Peter- Enid Blyton coined the name for her character PC Plod in the Noddy, Toytown children's books, taking the implication of slow, plodding intelligence to his persona and due to her phenomenal success as an author, with several generations of children brought into reading by her accessible style and prolific output, so Plod, Noddy, Big Ears, the Famous Five and the Secret Seven entered into the language. Blyton is much derided nowadays as she wrote of things that today we can't accept because their meaning has evolved or become anathaema - such as the evil golliwogs (black dolls that looked like caricature black face minstrels), Sambo, another black doll who was ostracised until a rain shower washed him white and characters with names like Dick & Fanny which were of course, perfectly normal and innocent names and characterisations when Blyton was writing around the 1930s to 50s.
I got the above by googling and I couldn't find a reference to the police being called Plod in earlier history
John