What is the best paint to use on plaster in a stone cottage, been told it needs to be able to breathe to help prevent damp getting locked into the wall
No synthetic paint will give you the breathability - the correctly term for walls is vapor permeability - of a mineral paint.
Synthetic paints (both oil paints AND latex emulsions) are made from oil distillates and will eventually bubble and peel because they are a moisture barrier. Even the so-called breathable ones have a fraction of the breathability of mineral paints.
Mineral paints are the best solution, they are non-toxic and ecological and the best choice for preservation of architectural heritage. They are antistatic so they do not attract as much dust, are alkaline so they never grow mold and rarely moss, are just as vapor permeable as stone, good for interiors or exteriors, withstands any temperature, does not release toxins over time, and do not release toxins even in a fire.
The cheapest alternative is
lime paint. This has been in use for millenia and many old buildings have suffered since it has fallen out of use. However, lime is not as durable to rubbing or scratching (stairwells, hallways, etc), weathering, acid rain, etc. This is because calcium is a very soft mineral. However, a simple lime whitewash is far cheaper than any other alternative. It cannot be applied on horizontal surfaces where water pools.
The best alternative for stone - it lasts much longer than any other type of paint, just as vapor permeable as stone, good for interiors or exteriors, is washable - is
silicate mineral paint Some are emulsions which contain small amounts of petroleum distillates and may offer a wider range of colors, others are pure minerals. These petrify into the stone and will last for decades, perhaps centuries, without a recoat.
If the cabin has already been painted with an oil or latex paint, the surfaces will first need to be stripped down to the stone before applying a mineral paint.