Someone tipped a few litres of paint into the corner of our garden — how bad is it and what should we do with that soil?

The first thing to establish is which kind of paint, because the two answers are very different and you may be able to tell by looking.

Emulsion / water-based, which is what most leftover household paint is: mostly water, a plastic binder, and mineral fillers like calcium carbonate and titanium dioxide. Once dry, the binder is essentially an inert plastic film. It is not something you want in soil, but it is not mobile and it is not especially toxic.

Solvent-based gloss or primer, or anything old: different situation, because of the solvent and because paint made before roughly 1990 may contain lead, and older still may contain more of it.

If what you found is a matt, chalky film that went on like thick milk, it is emulsion and this is a tidying job rather than a contamination event. If it smelled strongly, was glossy, or came out of unlabelled old tins, treat it more carefully.

On how far it travels: much less far than people expect, and that is the useful part of your question.

Paint is a suspension of solids in a carrier. When it hits soil, the carrier soaks in and the solids are filtered out almost immediately by the top few centimetres — soil is very good at this, which is the same property that makes it clean rainwater. A poured spill typically ends up concentrated in the top 5-10cm directly beneath it, with a sharp edge.

Lateral movement is smaller still. Without a slope or a lot of running water, you are talking centimetres, not metres.

So a bed six metres away is not at risk in any realistic reading, and it is not something to test or worry about. The affected zone is roughly the visible patch plus a small margin.