We present spectroscopic follow-up observations of 68 red, faint candidates from our multi-epoch, multi-wavelength, previously published survey of NGC 2264. Using near-infrared spectra from VLT/KMOS, we measure spectral types and extinction for 32 young low-mass sources. We confirm 13 as brown dwarfs in NGC 2264, with spectral types between M6 and M8, corresponding to masses between 0.02 and 0.08$M_{odot}$. These are the first spectroscopically confirmed brown dwarfs in this benchmark cluster. 19 more objects are found to be young M-type stars of NGC 2264 with masses of 0.08 to 0.3$,M_{odot}$. 7 of the confirmed brown dwarfs as well as 15 of the M-stars have IR excess caused by a disc. Comparing with isochrones, the typical age of the confirmed brown dwarfs is $<$0.5 to 5Myr. More than half of the newly identified brown dwarfs and very low mass stars have ages $<$0.5Myr, significantly younger than the bulk of the known cluster population. Based on the success rate of our spectroscopic follow-up, we estimate that NGC 2264 hosts 200-600 brown dwarfs in total (in the given mass range). This would correspond to a star-to-brown dwarf ratio between 2.5:1 and 7.5:1. We determine the slope of the substellar mass function as $alpha = 0.43^{+0.41}_{-0.56}$, these values are consistent with those measured for other young clusters. This points to a uniform substellar mass function across all star forming environments.
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