In a post on Twitter, guitarist Marr quipped that he had forbidden Cameron from liking his previous band.
In an open letter to fansite True To You, Morrissey said: "I would like to try to explain why I think Johnny is right not to be flattered. It is true that music is a universal language - the ONLY universal language, and belongs to all, one way or another.
"However, with fitting grimness I must report that David Cameron hunts and shoots and kills stags - apparently for pleasure. It was not for such people that either Meat is Murder or The Queen is Dead were recorded; in fact, they were made as a reaction against such violence."
In the wide-ranging letter, Morrissey also insulted "so-called royalty" including the Queen, who he said is "indifferent" to the killing of brown bears, adding that no-one could "remember or repeat a single word ever spoken by the Queen, such is her command of communication".
He added: "Prince William - who has never made the faintest imprint on the English soul - is also a hunter of deer, as is his fiasco (fiancée) Kate Middleton... although William and Kate are so dull as people that it is actually impossible to discuss them."
He also criticised "Bryan Ferret" (Brian Ferry), his son "Odious" (Otis), Jamie Horrible (Jamie Oliver) and "the dim-witted and good-natured David Peckham (David Beckham)".
Of Beckham, he added: "David Peckham is so dull that he is yet to master his first words."