Published Saturday, 13 October 2012
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Speaking at the Progressive Unionist Party's annual conference in Belfast on Saturday, he said he "would love to see" total paramilitary withdrawal.
"Not just in terms of decommissioning but in terms of people's perceptions, that even though it's happened they are still frightened," he commented. "Although they've withdrawn they haven't. They haven't gone away you know.
"I've spoken about low crime and what we are doing, but I do genuinely believe that's just a start, provided that we can take a step back and make the PSNI the only legitimate authority," the Chief Constable added.
Mr Baggott, who was the guest speaker at Saturday's event, said the PSNI had put 700 officers into deprived areas in an attempt to gain the trust of locals.
"I want your communities to trust us," he said. "The only way to get people to trust us is to tell them that when they phone us it's serious, even if it's not a serious crime matter.
"Because for some, antisocial behaviour blights their lives entirely and if we do not do that, it gives a legitimacy to other people to step into that gap and we need to be the legitimacy in Northern Ireland."
I do believe the PSNI has earned a legitimacy and a right to be the sole authority in Northern Ireland exercising its role in terms of presenting facts. At our heart is the protection of the most vulnerable.
He said the parading issue in Northern Ireland was being used as a "political football" and that decisions about marches were political, rather than policing, decisions.
"I do not think there's space anymore for competing authorities on this. If there's to be a debate about the Parades Commission, then that's a political debate. It's not one for the Chief Constable," he added.
The PUP, which has just two Belfast City Councillors, claims to be undergoing a restructuring process and hopes to reengage with working class loyalists.
Leader Billy Hutchinson said politicians who talk about high unemployment rates and poverty are not connecting with those in the deprived areas.
He discussed health, corporation tax and education and said the cultural identity of those his party represents must be considered.
"We are perceived to be sectarian bigots and we are not," said Mr Hutchinson.
"We need to get the language right and we need to challenge those people who are actually running us down.
"Working class Unionists and loyalists are not to blame for every problem that exists in this society but do you know what? They have the problems of this society," he added.