Where can one buy such stones? I can't seem to find anything like this in the UK.
First off, I'm thankful that anyone posted anything at all, to this. I was resigned to having put out a matza ball for which no one cares. So thanks for that, Ralprmartin, Gregg. And T3s, thanks for the thanks.
Answer: I don't think you can buy an arkansas stone like this from a store. (And I highly recommend soft arkansas stone for this).
What I did was buy some diamond plates for $4.00 each from Ebay China. I suggest 240ish the way to go for a soft ark. Then you use your eye.
People today stress out over how do you make sure it's "perfect?" There is no perfect. The stone will take the shape of how you use it. And the only reason (IMO) that it is curved in the long axis, at all, is just maintenance. If you take a stone nearly flat (or even flat) in the long axis, and you try to maintain the shape like that through use, your margin of error is tiny before the natural wear causes localized dips. If you start with enough curve for that material and how you use it, you will have the same error/tolerance in how it wears, but that shape you are aiming to maintain is curved enough where you don't get dips or "reverse curves" in the stone through this margin of tolerance/error. It is off by just as much, but it's still positively curved, everywhere.
As Jarrod says, "there's something magic that happens when every part of the stone can positively touch every part of the bevel."
If you curve the stone too much (I have experimented with that), what happens is you just end up using a smaller area of the center of the stone, because your wrist/arm/overall-movement range is not enough to use that whole curve efficiently. And the stone will wear down to the flatter shape, naturally. You're just getting it roughly into shape with the diamond plates. It's not, as we say, rocket science!
A 240 grit diamond plate makes quick work of the soft ark. Not a big thing. Just do it under running water.
This is really awesome for knives, esp. Because when you do the belly to tip, you start on the side of the stone and end up on top. That follows the edge automatically. You don't have to chicken wing your elbow out to follow that curve. It's like using a rod, but one where you have more area on top to not round off the tip.
This curve doesn't make the arkansas magically able to do anything, though. On blade with a large enough bevel area and/or hardness of the steel, you will exceed the limits at some point. E.g., I can't do the whole bevel on my 3/4" chisel, for instance; I'm just sharpening the edge bevel of the compound bevel. If I try doing the whole bevel, I can feel the metal start to glide over the stone. In this case, if you feel it's not cutting well, stop doing it! You're wasting your time, and this will glaze the stone, and then you have to do something to get it working, again. Just go to your coarser stone at that point.
The other no-so-obvious benefit is that the oil stays on the stone. You don't need as much. When you sharpen a straight edge on a flat stone, you squeegee the oil back and forth. It is messier and or takes more frequent application.