Where available, I've always found child labour handy for this sort of task. It's organic, has no chemical runoff into other areas, and is modestly priced.

Besides that, if you can make the cobbled area less shady or less damp that might help.

Where no child labour is available the RHS recommends acetic acid (Algon Organic Path & Patio Cleaner) for liverwort - otherwise it is a down on the knees job with a wire brush.

Permanganate of Potash (purple coloured crystals) is recommended for liverwort. I have not used it myself but fellow alpine gardeners water it onto their pots of seedlings when they get liverwort invasion, so it can't be too bad for the plants. Suppliers are listed on Google

Hi, I haven't used permanganate of potash or years, but you used to be able to go into any chemist shop, and buy a small tub of these crystals very cheaply, and they last quite a while because you only need a few crystals in 4 or 5 litres of water, they colour the water very quickly, and that is all you need to water onto your plants.
Also, for anyone who gets sweaty feet, put a few crystals into a bowl of water, and soak your feet for 10 minutes or so, Derek.

Great for preventing liverwort between the toes...

lol!

Two questions Derek - Does it work on moss, and
doesn't it stain the patio? I remember it makes horrible brown stains if you get it on your hands. We used to use it for treating fungus on goldfish.

Hi Sue, had a good laugh at your first comment, in answer to your second, yes it will kill moss, and it shouldn't stain if used in the right dilution, but if it does stain, you can remove it from anything with sodium bisulfite, Derek.