You should go back and re-read, or perhaps read it, that is. Mill doesn't deny the existence of objective truth, and for that matter, neither do I. What he does explicitly reject are appeals to objective truth, and those are piling up pretty deep from the "objectivists" and non-objectivists alike here...
"It is proper to state that I forego any advantage which could be derived to my argument from the idea of abstract right, as a thing independent of utility." - J.S. Mill