Some background: I'm reading "Narrative of a Journey to the Shores of the Polar Sea in the Years 1819-20-21-22" Volume One by John Franklin, published by Scholar Select. It's a collection of Sir John Franklin's journals, but he uses miles as a measurement and not kilometers.
Did other British captains do this?
The Nautical Mile is a long standing international standard for nautical and aeronautical navigation, even in nations which use metric and have for years. It was first standardized by the Admiralty, but has essentially spread worldwide and was more than a century old precedent by the time Franklin set sail. As part of his early training and to pass examination Franklin would even have had to learn much of the geometry and trigonometry that underwrote finding the distance, as part of his training in navigation for fixing a ships position by one of several means including sighting the sun, taking positions of stars, and of course good old dead reckoning based on ship heading and speed over time.
While we should note at the time the Metric system was still in its cradle, being that weird system the French championed in the midst of Revolution, along with of course a totally new calendar, and which Napoleon had even tried to change again. And the British nation was still over a century from full metric adoption.
It is not the same as a statute/modern US mile of 5,280 feet. It is instead the length of a minute of latitude, or 1/60 a degree of latitude. That translates to about 1.15 statute miles or about 6,080 feet. A Cable then is 1/10 of a NM, and a Fathom is 1/100.
For speed then a modern Knot is 1 NM/Hr.