Apologies for the relatively brief response – this might have been a question suited to the "Short answers to simple questions" thread, so I hope the mods will allow it.

The term "seven seas" has a very long history – it dates back to antiquity and seven is, of course, a sacred number in many places. As such, it has referred to a number of different waters over time, typically those most likely to be encountered by the sailors of the region in which the phrase was common. For the ancient Greeks, for instance, the seas were the Mediterranean, Aegean, Adriatic, Black, Red and Caspian Seas, and the Persian Gulf.

For the British, who from the 1700s had begun spanning much of the world's oceans, the "Seven Seas" were by the 19th century commonly taken to mean a different group of waters. Rudyard Kipling, who as the informal poet laureate of empire has perhaps as much claim and any to offer an "official" definition of the term as it was understood in Britain in the period you are interested in, wrote a book of poetry entitled The Seven Seas (1896) which celebrated the world-spanning empire of that period, and which used the term as a metaphor for that global dominance. In 1917 he wrote to a correspondent that he meant the phrase to cover the North and South Atlantic, the North and South Pacific, the Arctic and the Indian Oceans, plus the Mediterranean Sea. Kipling commented: "It’s an unscientific system but it covers all the seas with which our Empire and Army is concerned."

Source

Kipling to Captain C.A. Robinson, 29 Aug 1917, Letters of Rudyard Kipling 4, 468