I love horses and cavalry.
Notice how the gentlemen sits in his horse. This posture is very rarely accurately portrayed in almost every mini I have ever seen sculpted.
The back is somewhat arched, the shoulders thrown slightly backwards, the head erect and the ball of the foot placed on the stirrup.
The foot placement is especially significant. No one, and I mean no one, accurately sculpts the correct placement of the foot in the stirrup, which, with an English stirrup should be the ball and not the arch resting on the stirrup. The placement of the arch of the foot in the stirrup (which is always used by sculptors) is characteristic of the Western saddle, but totally incorrect for the English saddle.
The Empress minis (I have them and have painted them) are fairly close, especially the Sargent and the Officer. However, they both sport carbines and pistols and no swords. Still... they are probably the closest you will find.
Cheers.
I suspect that the sword is purely a ceremonial addition and I've no date for the photo. The alternate headgear would be the cap that is commonly seen today, the pillbox style being phased out in the early 1900's. WW1 British cavalry might be an option for these.