I don’t understand the button confusion. Small button, small flush. Big button, big flush.
The cheap toilets take two flushes to accomplish the task. Those are the culprits.
Maybe putting pictures on the buttons would help the Brits? Beer

on one button and bangers and mash on the other.
Just some "2 Button Toilet" reality here, for those of you who haven't experienced one of these total worthless farces. I had one. "Had" being the key word in that sentence.
They save nothing. But they add aggravation...... Lot's of it. Like the article said, they waste far more water than they "save". First off, there isn't much difference between the amount of water used between the #1 and #2 flush. It's a come on.
Second, and more importantly, the amount of water used for a "#2 Flush" simply isn't enough. And I don't care what model you buy. It won't change the plumbing, or the water pressure in your house.
If you don't flush at least twice you'll end up with about a 40% chance of clogging the thing if you leave a good sized, "deposit". So in order to get around that you have to crap and flush, when wipe and flush. And there goes the "savings". Right down the drain with your crap.
And that is assuming you left, "a good firm one". If it was a, "soft and smeary one", you could end up flushing the stupid thing 3 times or more, depending on how much paper you use...... And what kind.
While the nice, thick "super soft and absorbent" paper is great to use, it is far more likely to clog. And to make matters worse, the buttons are on the top of the toilet tank. So you have to twist yourself around, and reach behind you, to flush the stupid thing.
If you've ever had to deal with a bowl clogged with crap and paper, especially when you're not done yet, it's not one of life's more pleasant "treats". Especially if you create any backsplash while trying to clear it. Even the most inquisitive dog will be smart enough to depart the area. Leaving you alone to fend for yourself.
I was so sick and tired of dealing with it, I was just about ready to tear the thing out. Fortunately we ended up selling the place before I had to. This place has "normal" toilets, that you can get a little more powerful flush by just holding the lever down for a few seconds. I have yet to have one clog.
There are some things in life that must go smoothly. Taking a crap is one of them. I'll "save water" elsewhere. The synopsis here is "2 Button Toilets" save about as much water as those stupid water restrictor washers they put in shower heads.
All they do is increase the shower time...... And complaining. Especially if you live in a house with a woman with long hair. Luckily a cordless drill can remedy those in 5 minutes. And you're back to living a normal life.