Context. The H3O+ molecule probes the chemistry and the ionization rate of dense circumnuclear gas in galaxies. Aims. We use the H3O+ molecule to investigate the impact of starburst and AGN activity on the chemistry of the molecular interstellar medium. Methods. Using the JCMT, we have observed the 3(2)(+)-2(2)(-) 364 GHz line of p-H3O+ towards the centres of seven active galaxies. Results. We have detected p-H3O+ towards IC 342, NGC 253, NGC 1068, NGC 4418, and NGC 6240. Upper limits were obtained for IRAS 15250 and Arp 299. We find large H3O+ abundances (N(H3O+)/N(H-2) greater than or similar to 10(-8)) in all detected galaxies apart from in IC 342 where it is about one order of magnitude lower. We note, however, that uncertainties in N(H...