Deputy Chief Constable Terry Woods said: “I am angry and appalled at this abhorrent abuse of responsibility and trust.
“We commend the bravery of this young victim for coming forward.
“We apologise to her family and know nothing will ever undo the harm Dempster has caused to his victims.”
He said Dempster, who also admitted two counts of misconduct in public office, “represents the very worst of society”.
“He is not a police officer; he is a child sex offender, a criminal, and he has no right to be near police uniform or serve the public,” he said.
“Dempster is a depraved exception who we have wasted no time in dismissing and disowning.”
At Dempster’s disciplinary hearing, Chief Constable Stephen Watson, said: “It is this most egregious breach of trust of an innocent young child that is the most upsetting aspect of this case.
“I consider this case to be among the most distressing ever presented to me, such is the despicable betrayal of all that is inherent in being a decent police officer.”
An NSPCC spokesperson said: “As a police officer, Dempster’s role was to protect the vulnerable.
“Through his training and work he would also have been aware of the profoundly harmful impact that child sexual abuse can have on victims.
“Instead he sexually abused a young girl whilst on duty, took indecent photographs as a responding officer and downloaded thousands of child sexual abuse images of children, all of which was a devastating breach of trust that was placed in him.”