Natural products are attractive components to tailor environmentally friendly advanced new materials. We present surface‐confined metallosupramolecular engineering of coordination polymers using natural dyes as molecular building blocks: indigo and the related Tyrian purple. Both building blocks yield identical, well‐defined coordination polymers composed of (1 dehydroindigo : 1 Fe) repeat units on two different silver single crystal surfaces. These polymers are characterized atomically by submolecular resolution scanning tunnelling microscopy, bond‐resolving atomic force microscopy and X‐ray photoelectron spectroscopy. On Ag(100) and on Ag(111), the trans configuration of dehydroindigo results in N,O‐chelation in the polymer chains. On the more inert Ag(111) surface, the molecules additionally undergo thermally induced isomerization from the trans to the cis configuration and afford N,N‐ plus O,O‐chelation. Density functional theory calculations confirm that the coordination polymers of the cis‐isomers on Ag(111) and of the trans‐isomers on Ag(100) are energetically favoured. Our results demonstrate post‐synthetic linker isomerization in interfacial metal‐organic nanosystems.