Superconducting Nanowire Single Photon Detectors (SNSPDs) based on Nb0.15Re0.85 disordered nanowires are developed. The devices have a meander structure of wires 50 - 100 nm wide and cover a circular detection area with a diameter of about 10-16 μm. The main figures of merit of the detectors are extracted from a flood illumination process at 2.8 K, featuring a saturated internal efficiency up to λ = 1301 nm, recovery times between about 8 and 19 ns, and a jitter of about 35 ps. These results confirm that Nb0.15Re0.85 is a promising candidate for the realization of fast SNSPDs, as recently suggested.