Jeremy Brett loved horses and loved to ride. His social class and education alone would’ve meant he would’ve been a competent rider, regardless. You can see this love for horses in all his interactions with them in the TV show. Always time for a pat or a hello and of course a ride or two.
I laugh because his equitation is sloppy. He clearly know what he’s doing. He’s extremely comfortable with his riding. His horse has no objection to anything he does, but he’s sloppy.
Hardwicke is…correct. But the difference between them is still significant even it’s all in the details. In the first two gifs, Brett is sitting the trot. A sitting trot isn’t easy, physically, your core has to do a significant amount of work to stabilize you against the movement of the horse at the same time your hips need to be flexible enough to follow the motion. His horse’s back doesn’t have a lot of up and down motion so he may be sitting it because he’s encouraging the horse to trot slower or he’s being lazy and slowing the horse to a walk here. Look though at how relatively still his hands are.
Contrast this with Hardwicke who is pulling(?) himself up to a rising trot? In a rising trot you let the motion of the horse’s gait push you out of the saddle, then you control your fall back to it only to be pushed out again. With a horse that is carrying you, a nice rising trot is near effortless for the rider. This isn’t effortless. Now, some of that may be the horse, but a lot is him. He’s fighting the motion and isn’t at all in synch. And look at his hands, flopping all over. You can not communicate via the reins effectively if they’re flopping all over like that.
In the next set of gifs you can see Brett doing a rising trot. Look at how effortless the motion is compared to Hardwicke who is essentially pumping himself in and out of the saddle. H is centered though and for all his mess, he’s not interfering with the horse. To me this is more about lack of miles in the saddle, not a lack of correct instruction. He’s correct in his riding, but he’s not practiced. Brett is practiced to the point where he’s sloppy because he comfortable enough to cut corners.
You can see that sloppiness when he dismounts in that gif, his heel catches the rein because he’s being a show off and dismounting like a young gentleman just returned from a a gallop across the estate on his new horse. But the horsemanship is there. He immediately catches it, fixes the equipment, and strokes the horse. Who clearly thinks he’s silly, but isn’t mad.
And finally, the gallop. This is actually the most comfortable I’ve seen Hardwicke look, which is what made me realize that he’s just not practiced and probably doesn’t love riding the way Brett does. Perhaps he didn’t have the opportunity to ride often when he was young, perhaps he didn’t care. But somewhere along the way he picked up instruction on riding. He’s correct. His horse stumbles a bit, probably tripped slightly, and you can see him brace himself, but he doesn’t snatch at the horse’s face or come unseated at all. His arms are still flopping but he’s holding his shoulders which means he has the core control he needs to remain balanced. He’s not a bad rider, just needs more miles in the saddle.
Here though in these last two gifs Brett’s sloppiness is on full display. Observe how his elbows remain close in to his body (especially compared to Hardwicke) but his legs are flying all over. He’s bracing quite a bit. At one point you can see him pull his horse to the right, most direction cues are from the seat so he’s probably already asked nicely with no result and is now telling the horse to turn. This sort of heels way down and brace is actually a bit of a protective seat for galloping cross-country on something hot. In this position you have a fair amount of leverage to pull a horse up - your sacrificing correctness for strength at this point.
Now here’s the thing, this sloppiness may be part of some defensive riding on Brett’s part and understandable in the circumstances. Even though his equitation may not be perfect, he’s still riding very well. In this gif the horse doesn’t look like he’s doing anything that warrants this defensiveness on Brett’s part, but something caught my eye, he’s (the horse) is wearing a standing martingale in the 2nd set of images. I can’t tell if he is in the first or last, but with the way he tosses his head in the first, I’d say he is. Standing martingales are essentially a strip that connects the bridle to the girth by passing through the legs. A second strap is looped onto it about halfway and wraps around the neck. In the hunt discipline which is what Brett would’ve grown up riding (although more literal hunt) it’s considered correct tack and a piece of necessary safety equipment. It keeps the horse from tossing it’s head and smacking you in the face (as a person who has received a bloody nose this way, yes, it’s far more common than you’d think) and the collar around the neck can be an “oh shit” handle.
Hunt means literally that, galloping across fields and jumping hedges and ditches and gates and rock walls. People who ride like this often ride in a very defensive seat. Hunter horses tend to be a bit hot and need to be very brave. They tend to be forward which means they usually don’t need to be encouraged to go. They just do, you as the rider simply manage what they give you.
It’s possible Brett insisted on a standing martingale because that’s what he considers correct tack and what he would’ve considered correct tack for Holmes (he was a stickler for such things). But in my mind, it’s also equally likely that he saw this spunky little horse that looked like he was up for some fun and Brett said “I want to ride that one.” It was fun to see him obviously enjoy himself and I bet that horse was fun to ride. Who cares if Brett could’ve had quieter legs, he was clearly having a good time and the horse didn’t seem to mind in the slightest.
Anyway. That was a fun bit of analysis. Thank you @sanguinarysanguinity.