Bob, interesting information, I am very familiar with Whitworth rifles and you are right, they were and are very accurate. I may have misspoke, I doubt EVERY British Soldier had to qualify at 1250 yards, my understanding from the article I read was that marksmen had to be able to hit that sized target at least a few times within what I believe was a 2 minute interval to qualify. In an article at www Military Factory.com regarding the P 1853, they state a "trained" user (whatever that means) could fire between 1 to 3 aimed shots at 2,000 yards. I assume that is in a minute. They do not give a target size. When I was younger, I participated in competition with a similar sized target myself at 1000 yards using my Enfield reproduction. I even hit the target occasionally! The gun could certainly do the job if the trigger actuator did not malfunction. I seriously doubt I would qualify for anybody's army any more at my age!
Here is a copy and paste on the Enfield regarding the standard sights.
The Pattern 1853 Musket was among the first military muskets to be fitted with sights as standard (Muskets previously had been inaccurate, due to the smoothbore barrel and musket ball, and therefore could only shoot an effective range of 200 yards at the most, a distance of which sights are not necessary). The Pattern 1853 Enfield used an adjustable ladder sight, with increments at:
◾100 yards (91m)
◾200 yards (180m) - Default / 'battle sight'
◾300 yards (270m)
◾400 yards (370m)
A second, flip up sight was used for distances between 900 (820m) yards to 1,250 (1,140m)yards.
This would certainly indicate they at least trained at that range. Plus, most references I have seen list the maximum effective range as 1250 yards, which as you know is the range at which aimed fire will have effect. My personal opinion, which is worth just what you pay for it, is that when the rifled musket came into use, and was an effective killing tool at ranges greater than 1000 yards, they probably trained their soldiers at those ranges, especially after the Crimean War. Of course, in a battle situation, it is doubtful anybody could aim and hit a target at those ranges.
As far as bullet diameter goes, I have several original Enfield Minie balls in my collection that were imported from England during the late unpleasantness, they all mike out around .574 and .576 so I imagine they must have addressed the issue you pointed out with undersized bullets affecting accuracy.
Remember too, the British army at that time was quite small and was very professional. The British army has always been known for outstanding marksmanship. In 1914, when the "Old Contemptibles" faced the Germans at Mons, the Germans thought they were being faced by machine guns because the British Infantry was so accurate with rapid fire at long ranges. Granted, those were with modern weapons but the training standards were decades old.