It’s almost 100 years since the music-hall artist Charles Penrose wrote and performed the still-popular The Laughing Policeman: “He’s too kind for a policeman/ He’s never known to frown/ And everybody says/ He’s the happiest man in town.” But the idea that the constabulary may not take their duties seriously enough still seems to be an issue today.

This week, Derbyshire police tweeted a jokey picture of a cordoned-off flip-flop belonging to an alleged criminal who had legged it after his car was stopped by the police. Cue inevitable outraged response that the police should not be larking about on Twitter when there are serious crimes to be investigated.

It is not a new thing. A year or so ago, Barrow police tweeted that they had received a report of the theft of perfume from Asda and “WeScentOfficersToInvestigate.” Ho-ho. And Greater Manchester police have also tweeted some less-than-sombre items such as: “Male riding moped Princess St found to have no insurance and now has noped.”

Police use of Twitter also featured when Jeremy Clarkson complained last month that he had been held up in the wake of a fatal accident in Hammersmith, west London, because the road had been closed for a long time. An officer responded: “Sorry you were delayed @JeremyClarkson – perhaps you’d like to come with us and personally explain to the family of the deceased that we didn’t investigate the death of their loved one thoroughly because you wanted to get home?” Ouch.

Crime is often a grim and serious business, so there has to be some room for levity to deal with it all; the phrase “gallows humour” didn’t come from nowhere. The police would also argue that engaging with the public through Twitter makes it easier for them to get publicity when they need help in identifying suspects or solving crimes. Ever since the Leveson inquiry, in the wake of the News of the World’s malpractices, there has been a nervousness within the police of any kind of publicity. It would be sad if a touch of light-heartedness led to a renewed froideur.