In the TV series "I, Claudius," at least, the filmmakers were following the lead of the novelist on whose books the series was based, Robert Graves, who (among other things) was satirizing the British ruling class by how he told the story of the Roman ruling class (just as Gilbert and Sullivan's "Mikado" and "Utopia Limited" are really all about making fun of Britain, not Japan or Hawaii).

The novels, of course, don't depict a "British accent," but they depict other aspects of upper-class Britain, and the Received Pronunciation accent or somethign like it would be pretty much mandatory for any stage or film version of the novels.