Current antibody-drug conjugates (ADCs) target internalising receptors on cancer cells leading to intracellular drug release. Typically, only a subset of patients with solid tumours has sufficient expression of such a receptor, while there are suitable non-internalising receptors and stroma targets. Here, we demonstrate potent therapy in murine tumour models using a non-internalising ADC that releases its drugs upon a click reaction with a chemical activator, which is administered in a second step. This was enabled by the development of a diabody-based ADC with a high tumour uptake and very low retention in healthy tissues, allowing systemic administration of the activator 2 days later, leading to efficient and selective activation throughout the tumour. In contrast, the analogous ADC comprising the protease-cleavable linker used in the FDA approved ADC Adcetris is not effective in these tumour models. This first-in-class ADC holds promise for a broader applicability of ADCs across patient populations.