Essentially this is because of the army sticking to the official standard weights and measures of ordnance that was in use from 1764.

In the 18th century, cannon was measured by the weight of the shot instead of calibre.

In 1919 the standard was updated to include metric measurements of calibre, but official designations continued to use weight measurements (which were only rough approximations). It was also helpful in distinguishing between pieces which whilst the same calibre, had smaller or larger projectiles. Such as the 12, 13, 15 and 17 pounders, designated for different roles, with differently weighted shells, nonetheless they had the same calibre.

The standard was established originally by the Master General of Ordnance, a senior position in the British army which dates back to about 1415 and still exists today. Although it was abolished between 1938 and 1959.

It gets confusing when you start looking at Naval armaments. A George V class battleship was equipped with a range of cannons, but included multiple 2 pounders, large, 14inch (that's 360mm) naval cannons (firing 1,590lb shells) and both 20mm and 40mm anti aircraft cannons (albeit they were both imported).

These days artillery used by the army is measured in mm, but naval cannons/guns are still measured in inches, anti aircraft guns in mm.

I guess fifteen hundred and ninety pounder is a bit of a mouthful.