Aims. 2P/Encke is a short period comet that was discovered in 1786 and has been extensively observed and studied for more than 200 years. The Taurid meteoroid stream has long been linked with 2P/Encke owing to a good match of their orbital elements, even though the comet’s activity is not strong enough to explain the number of observed meteors. Various small near-Earth objects (NEOs) have been discovered with orbits that can be linked to 2P/Encke and the Taurid meteoroid stream. Maribo and Sutter’s Mill are CM type carbonaceous chondrite that fell in Denmark on January 17, 2009 and April 22, 2012, respectively. Their pre-atmospheric orbits place them in the middle of the Taurid meteoroid stream, which raises the intriguing possibility that comet 2P/Encke could be the parent body of CM chondrites. Methods. To investigate whether a relationship between comet 2P/Encke, the Taurid complex associated NEOs, and CM chondrites exists, we performed photometric and spectroscopic studies of these objects in the visible wavelength range. We observed 2P/Encke and 10 NEOs on August 2, 2011 with the FORS instrument at the 8.2 m Very Large Telescope on Cerro Paranal (Chile). Results. Images in the R filter, used to investigate the possible presence of cometary activity around the nucleus of 2P/Encke and the NEOs, show that no resolved coma is present. None of the FORS spectra show the 700 nm absorption feature due to hydrated minerals that is seen in the CM chondrite meteorites. All objects show featureless spectra with moderate reddening slopes at λ < 800 nm. Apart for 2003 QC10 and 1999 VT25, which show a flatter spectrum, the spectral slope of the observed NEOs is compatible with that of 2P/Encke. However, most of the NEOs show evidence of a silicate absorption in lower S/N data at λ > 800 nm, which is not seen in 2P/Encke, which suggests that they are not related. Conclusions. Despite similar orbits, we find no spectroscopic evidence for a link between 2P/Encke, the Taurid complex NEOs and the Maribo and Sutter’s Mill meteorites. However, we cannot rule out a connection to the meteorites either, as the spectral differences may be caused by secondary alteration of the surfaces of the NEOs.