The experimental data were taken in the NanoPhotonics Group at the Cavendish Laboratory (University of Cambridge). The dataset is for the journal article, "Quantum electrodynamics at room temperature coupling a single vibrating molecule with a plasmonic nanocavity". The photoluminescent spectra were taken with an electron multiplying charge-coupled detected (EMCCD) (Andor iXon) and the photon correlation measurements were taken with single photon avalanche photodiodes (MPD). For further description of the setup, see the Method section of the manuscript. We acknowledge support from EPSRC grants EP/G060649/1, EP/L027151/1, EP/G037221/1, EPSRC NanoDTC, and ERC grant LINASS 320503. O.S.O acknowledges the support of Rubicon fellowship from the Netherlands Organisation for Scientific Research. R.C. acknowledges support from Trinity College, University of Cambridge.