Greatness can mean many things. Allow me to add a foreign (Swedish) perspective. From BBC Music's list, only Britten and Handel (whom we many will consider German) are regularly performed here. Even Elgar would be considered something of a rarity. At most ten would be recognised names among general listeners to classical music, and then often for something like "When I am laid" or "Greensleeves" being played once in a while on radio. Compared to Germany, Italy or even France British music is rare, and ranking the greatness of most of those mentioned in this correspondence would be beyond the average listener, as exposure to them is a matter of chance - for instance a British conductor or broadcaster marketing them.
It's probably similar if British listeners - except for enthusiasts writing for MusicWeb International - ranks Scandinavian composers beyond Sibelius, Grieg and maybe nowadays Nielsen. Few Swedes would consider any Swedish composer "great" in the sense we think of Britten or Handel great.
Once we add names beyond the top 100 or 200 on a global list there may be room for people like Vaughan Williams or Stenhammar, but it seems meaningless to rank them as the field grows so much larger when we leave the top echelon.