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To reload they would roll onto their back to get the rifle in a good position and then back again to get the cartridge like the figure bottom 3rd from right and so forth.
The procedure from the normal standing position is on this web site:
http://www.militaryheritage.com/enfield1853.htm
To carry out all these procedures and maintain reasonable safety (different if you were as one of a pair and relatively isolated) would be difficult in a prone position. The rifle could be loaded kneeling or sitting then the cap and full **** procedures done in the prone position. Skirmishers ( more like snipers) often worked in pairs at Sebastopol, so one kneeling and one prone resting against sand bags(like tiny redoubts or sangars) is a possibility. These would be maintaining the outposts and preventing small scale incursions which was a constant feature of the Crimean war once the siege had been established. Several of the other figures also look ideal for this role.
As David says, prone firing was done by skirmishers in the Crimea and ACW, and accuracy was never an issue - aside from the dense smoke raised by firing black powder weapons. Indeed, firing prone only increased accuracy; the major drawback is, reloading in this position slows your rate of fire way down to about one round a minute or less, particularly if you have to force the bullet down a rapidly fouling barrel, which is why skirmish drill involved groups of four men, working in pairs, and kneeling behind whatever cover was available was preferred over prone shooting