What I'm looking for is something that can be used as a miniature
gutter to direct water from the edge of an object towards somewhere
more appropriate for it to end up.

A simple round bottomed 'j' section that's about 25mm wide across the
bottom and at least 30mm high would be perfect. The length needs to be
about 3 metres. It needs to be weatherproof, so white plastic or
extruded aluminium would seem like promising materials.

I had hoped that the local DIY sheds might have had something, I also
tried a specialist in PVC cladding materials.

Does anybody have a suggestion where such a profile can be readily
obtained ?