The distance to the Galactic Centre (GC) is of importance for the distance scale in the Universe. The value derived by Eisenhauer et al. (2005) of 7.62 +/- 0.32 kpc based on the orbit of one star around the central black hole is shorter than most other distance estimates based on a variety of different methods. To establish an independent distance to the GC with high accuracy. To this end Population- ii Cepheids are used that have been discovered in the \OG- ii and \OG- iii surveys. Thirty-nine Population- ii Cepheids have been monitored with the SOFI infrared camera on 4 nights spanning 14 days, obtaining typically between 5 and 11 epochs of data. Light curves have been fitted using the known periods from the OGLE data to determine the mean K-band magnitude with an accuracy of 0.01-0.02 mag. It so happens that 37 RR Lyrae stars are in the field-of-view of the observations and mean K-band magnitudes are derived for this sample as well. After correction for reddening, the period-luminosity relation of Population- ii Cepheids in the K-band is determined, and the derived slope of -2.24 +/- 0.14 is consistent with the value derived by Matsunaga et al. (2006). Fixing the slope to their more accurate value results in a zero point, and implies a distance modulus to the GC of 14.51 +/- 0.12, with an additional systematic uncertainty of 0.07 mag. Similarly, from the RR Lyrae K-band period-luminosity relation we derive a value of 14.48 +/- 0.17 (random) +/- 0.07 (syst.). The two independent determinations are averaged to find 14.50 +/- 0.10 (random) +/- 0.07 (syst.), or 7.94 +/- 0.37 +/- 0.26 kpc. The absolute magnitude scale of the adopted period-luminosity relations is tied to an LMC distance modulus of 18.50 +/- 0.07.