Using a tunable optical microresonator with subwavelength spacing, we demonstrate controlled modulation of the radiative transition rate of a single molecule, which is measured by monitoring its fluorescence lifetime. Variation of the cavity length changes the local mode structure of the electromagnetic field, which modifies the radiative coupling of an emitting molecule to that field. By comparing the experimental data with a theoretical model, we extract both the pure radiative transition rate as well as the quantum yield of individual molecules. We observe a broad scattering of quantum yield values from molecule to molecule, which reflects the strong variation of the local interaction of the observed molecules with their host environment.