Recent estimates of the Cepheid distance modulus of NGC 6822 differ by 0.18 mag. To investigate this we present new multi-epoch JHKs photometry of classical Cepheids in the central region of NGC 6822 and show that there is a zero-point difference from earlier work. These data together with optical and mid-infrared observations from the literature are used to derive estimates of the distance modulus of NGC 6822. A best value of 23.40 mag is adopted, based on an LMC distance modulus of 18.50 mag. The standard error of this quantity is ~0.05 mag. We show that to derive consistent moduli from Cepheid observations at different wavelengths, it is necessary that the fiducial LMC period-luminosity relations at these wavelengths should refer to the same subsample of stars. Such a set is provided. A distance modulus based on RR Lyrae variables agrees with the Cepheid result.