I should perhaps have specified that it's not only warships, but all ships, and not tonnage, but numbers. The Stuka had its way with allied shipping in the English Channel, North Atlantic (long range R version from Norway) and all sorts of coastal ships along the Mediterranean, Black Sea, Baltic Sea and Barents Sea (north of Finland). It is generally accepted (including by such knowledgeable people as Barrett Tillman) that the Stuka did indeed sink more vessels (merchant marine and warships, if counting by numbers of ships sunk) than any other aircraft. The Curtis SB2C is credited the greater tonnage, and the Douglas Dauntless with the most number of warships sunk.
The Swordfish sank about 200,000 tons of shipping. More then any other British aircraft. That would be an impressive figure if it happened over a few months, as with the Fw 200 and Do 217. But it is not very impressive when spread over 6 years of warfare. About the same as the Italian SM.79 from 1940 to '43.