What stops commercial ice lollies from being rockhard?

If they are rock-hard, they need more sugar (or you're one of those people that use artificial sweeteners and they don't have the same effect that sugar does.)

About 30% sugar is a typical proportion that works - feel free to experiment. i.e. mix 300g sugar with enough water and flavoring to make 1 liter of mixed solution. If using juices, calculate how much sugar they contribute from the label information and add enough more sugar to reach 30%

Pectin can also be helpful. You need things that interfere with the size of ice crystals. Jam is one way to get it, (and some sugar - again, read the label to find out how much) or you can get the pectin made for canning your own jams.

Popsicles are very easy to make at home, and regulating their hardness is very simple.

If the water content of the pop is too high, they end up extremely hard - like ice cubes.

Sugar and alcohol both help keep this from happening. By lowering the freezing point of the solution, they make the pop softer. Add too much, however, and the popsicle won't freeze solid enough to stay on the stick.

Once the pop is frozen it tastes much less sweet, so don't worry if the mix tastes too sweet before you freeze it.

Most fruits work pretty well with 1 pound puréed fruit, 3/4c simple syrup (boil one cup water and 1 cup sugar until clear). Watery fruits like melons benefit from more syrup, and very sweet fruits (especially canned ones) might need less (I use 2/3c syrup).

If you're going to add alcohol, use about 2 shots for 25 fluid ounces of mix. Any more, and the pop won't freeze correctly.

Pectin and gelatin also have an effect, but I find they give the finished pop a very strange texture - and they need sugar to set anyway.

In addition to using enough sugar, one other possible trick is churning the mixture - much like ice cream, mechanically breaking the ice crystals down to keep them small and the resulting confection soft.

I have had these ice pops, the simple tube-in-plastic ones, and caused this to happen. A few times, once the pop was frozen (depending on how slow it froze) the ice would be obviously crystalline. I once tried simply squishing the ice to break up the crystals, and re-freezing (since the act of crushing started to melt the pop). That pop was immensely soft compared to the simply frozen ones.

So, commercial ice-pop makers may well have access to ice cream churning equipment or the equivalent - and simply letting the ice pop liquid churn for a bit while (or after) freezing and before pouring into their final molds would result in much softer ice pops... and it is an extra step that most home ice-pop-makers wouldn't do, since the results of simply frozen ice pops are passable.

This also makes sense of the fact that, like ice cream, partially melted and refrozen commercial ice pops tend to have patches of harder, more crystalline ice. If the softer texture was only about the proportions of sugar or addition of stabilizers, melted and refrozen ice pops would probably still have that soft texture. The fact that texture is lost when melted and refrozen seems to suggest one of the factors that keeps the ice soft happens during the commercial freezing process.

I can't say what UK ice lollies contain, nor can I check what ingredients are included in popsicles in Canada where I live since I don't have smaller children and don't eat them myself. But I've made various frozen desserts and have incorporated some ideas from the chapter 'Ice Cream and Frozen Desserts' (from the Handbook of Food Products Manufacturing). It's free to download so I did as I wanted to learn more.

Food grade glycerin (there are vegan forms too) can be added to frozen desserts to lower the freezing point of the mixture so rock hard ice doesn't form. It's more effective at lowering the freezing point than other sugar alcohols and better and healthier than using high fructose corn syrup (HFCS) which also lowers the freezing point. That's why one finds it so often in commercial frozen desserts. Plus HFCS is much cheaper than glycerin (although that's changing) and manufacturers want to keep costs down.

Depending on how much sugar you use, I'd say something between 1/2 - 1 tsp glycerin to 1 cup of water or juice (not counting any added sugar) will give a softer but still frozen ice lolly. Sorry I can be more specific but other ingredients added to ice lollies makes it hard to be exact.