Although the local environment of a molecule can play an important role in its chemistry, rarely has it been examined experimentally at the level of individual molecules. Here we report the precise control of intramolecular hydrogen-transfer (tautomerization) reactions in single molecules using scanning tunnelling microscopy. By placing, with atomic precision, a copper adatom close to a porphycene molecule, we found that the tautomerization rates could be tuned up and down in a controlled fashion, surprisingly also at rather large separations. Furthermore, we extended our study to molecular assemblies in which even the arrangement of the pyrrolic hydrogen atoms in the neighbouring molecule influences the tautomerization reaction in a given porphycene, with positive and negative cooperativity effects. Our results highlight the importance of controlling the environment of molecules with atomic precision and demonstrate the potential to regulate processes that occur in a single molecule.