In 1964, A.D. Ridge in "Archive" (The Journal of the British Records Association) asked the same question about St Dunstan's Stepney and baptisms at sea in his paper "ALL AT SEA: OBSERVATIONS ON THE STEPNEY BAPTISM REGISTERS" The first page of the article can be read for free here. Thanks to Nic Donnelly for discovering the paper and to Andrew Millard for providing me with the full version.
The author looked through every volume of the baptism registers from their start in 1558 up to 1936 (that's dedication!). The first mention of a child being baptised at sea was 1893. There were a sprinkling of baptisms from then on each year, generally one or two up to 1936. The exceptions were in 1921 when a family of 6 were all baptised on the SS Bernina, and in 1922 9 boys were baptised together by the ship's chaplain while they were in training on the HMS Colossus.
Ridge then examined the ecclesiastical regulations. He concluded: "There is, however, no evidence among the extant parish records to show that St Dunstan's parish was ever given special rights and interests in the matter. The Legal Secretary and Registrar of the Bishop of London has in fact expressed the view that to the best of his knowledge neither the Bishop of London nor the Rector of Stepney has any special jurisdiction over the high seas: nor is the Bishop now concerned in licensing the chaplains of naval ships. It is significant that although there are references to two baptisms by the Bishop of London himself, there is also known to be at least one instance where he officiated and yet no record was kept. Surely if he had had a special jurisdiction he would have been punctilious about notifying his 'special registrar' at Stepney?"
If anyone wishes to know more about the methodology involved in compiling this paper, please contact me directly through the WikiTree messaging system, as the paper is still under copyright and I can't upload it for general viewing.
ALL AT SEA: OBSERVATIONS ON THE STEPNEY BAPTISM REGISTERS Ridge, Alan D, Archives (British Records Association); Oct 1, 1964; vol 6, number 32; page 229