Dear Alastair,
This has been a regular question, over the years. I attach a pdf of the press report (NY Times, June 15 1899) which describes Caroline carrying a porphyry urn, containing Josephine's ashes, aboard ship for the return to England. The NYT suggests that the ashes were to be interred in a family grave in Rottingdean, but there seems to be no record of a ceremony at the plot where Uncle Ned 's ashes had been buried the year before. It is worth remembering Rudyard's approval of that ceremony: 'There was no mobbing; no jabber; no idiotic condolences'.