Hi,
I'm not an attorney, and I'm not shooting in the UK....
But I do photograph this type of event, as the official photographer under contract to the organizer, and I think I understand quite well where the commercial photographer in this case is coming from...
It doesn't have to do with the fact that you took the photographs. As others have said, anyone can do that in a public venue, and in fact, in many private venues, so long as there is nothing prohibiting it. Bothersome, but not something that commercial photographer can really say much about.
Nor does it have to do with you displaying your images on your website. Again, a bit of a thorn in the side, but not something they can comment about.
It even has nothing to do with whether or not you offer the images you made for sale, if that's what you are doing on your website. That would be a slightly bigger thorn in the side, but still pretty much out of the other photographer's control.
I believe it boils down to just two things really at issue here:
One is common courtesy. More on that in a moment.
The other is that you have posted on the organizer's blog about your photos and, even if passively, promoted your work competitively against the contracted photographer's. This is bound to be in violation of the agreement between the organizer and their photographer. It's the organizer's blog, which they pay to put up online and maintain, and thus is theirs to do with as they see fit. You should remove your posting and images from that blog. If you don't, I imagine the organizer will.
Now, the official photographer still might ask you to remove your images from the Internet entirely (i.e., your own website) and maybe even threaten legal action, but I doubt they have any leg to stand on. It's probably just bluster.
But, the question of "what's right" is another thing entirely.
Please do have some respect for the guy who is trying to feed himself and his family with his photography, no matter what else you might think of him. This sort of work does not pay huge sums, there's not a lot of profit to go around, and a lot of the work is being done purely "on spec".
It's quite easy to drop in at a show and take 15 shots like you did. It's another thing entirely to arrive before the first competitors do and work at making photographs until the last ones leave in the evening, trying to get a good selection images of each and every one of them at their personal best, all the while toting around 30 lbs of camera equipment. Now do that at each of perhaps two to four events any particular organizer holds in a year, and in turn multiply that times a half dozen or more different organizers that a photographer might work with. You have to really enjoy the work to keep doing it and producing fresh images year after year.
Overall, I handle the hobbyist shooters at my events fairly easily. (Heck, I've even led groups of them there, as an instructor.)
I usually have access to areas that they don't. This allows me to get shots they can't.
I also use more professional equipment than the vast majority. (BTW, your "two grand" is just a drop in the bucket, even in Sterling, sorry to tell you.)
And, I have years of experience that helps me get better shots, sometimes using techniques they're unfamiliar with, other times just knowing more precisely when to press the shutter release, and all in the safest possible manner for the participants.
Still, it can be pretty disheartening to drive 50 miles pre-dawn to shoot a show that you've contracted for, work a 12 hour day knowing that there will be another couple days spent editing and uploading thumbnails from the 700 to 2000 images I'll take... And then have a "proud Dad/lawyer/photo hobbyist" show up driving his $80,000 Hummer H2 towing a $25,000 horse trailer with $30,000 worth of horse flesh inside along with another $10,000 in tack and costume changes for his 12 year princess... And totting a 1D Mark III with the price tags still hanging on it, and a bag full of L-Series glass, with which he shoots not only his daughter but everyone else's... At 10 frames per sec., so some are bound to turn out... Offering everyone there free prints of his photos!.
This is precisely what happened to me recently. And so far my print sales from that particular show don't cover the cost of gasoline getting there and back.... Let alone compensate me for the time I invested, put food on my table, help pay the rent or offer anything toward my mortgage payment, or insurance premiums, or eventual replacement of my cameras and lenses, or any of my other costs of living and doing business!
And, to rub salt in the wound, this guy who's giving prints away free "just for fun" could obviously very easily afford to buy prints from me. (I'm confident my shots are better.... For one, he obviously didn't know what "fill flash" was... Not that he could use it effectively at 10 fps, nor did he appear likely to know how to use it safely around horses.)
Now, this example was a new show for me, working with the organizers for the first time. It was on private property and I'd discuss the situation with them before agreeing to shoot another of their shows.
I have a couple other strategies to deal with proud parents with camera phones, or toting point n shoot digitals or, increasingly, D-SLR kits. None of my tactics are harmful or injurious in any way, but I won't go into the details here. 
Still, "Mr. Freebie" is pretty hard to deal with. 
At most of the venues I shoot, whether public or private, once they realized what he was doing the organizer would have pulled him aside and quietly asked him to have please some respect for others who are there working at their trade. That's a fair request, I think, even though I'm pretty biased. (After all, I'm not stopping his clients outside the door to his law offices and providing them free legal advice, in lieu of them paying his fees.)
Most organizers place a value on and are supportive of the photographer who is committed to being at all their shows, year in and year out, regularly providing high quality services to their participants/clients in a professional, affordable and safe manner. I never "share profits" or "pay a percentage", only rarely have paid a vendor fee up front or tithed part of my profits to a church. But I do help out organizers by allowing some use of my photos and in many other ways, whenever I can and it's to our mutual benefit.
I hope you'll excuse me now. I have back to back shows this coming Saturday and Sunday to prepare for.
Cheers!
