Mr Wright, Chairman of the Foyle UUP Association said the UUP leadership has the full support of the Unionist Association in Foyle.
He said the party would not be shaken from its resolve by "that reluctant Secretary of State, Shaun Woodward who one would have thought would have learned by now that the UUP is not a party of spongers."
In a statement on the Hillsborough Agreement Mr Wright said: "By making money available as he has done to sweeten the deal between the two biggest parties is to recognise the pressing need for additional financial support for policing and justice as a moral imperative and this case holds firm regardless of whether it is administered from Westminster or Stormont.
"If the money is withdrawn, then it is the government which will stand exposed not those who take principled positions.
"Why would the UUP, a party with an effective and commendable record in administering policing and justice in difficult times and in favour of its devolution in favourable circumstances, wish to see the service under-funded?"

Process and not product

He said the problem with the agreement was that it was about "process not product."
"It is short on detail and in places is mere aspiration. Policing and Justice is far from settled.
"Sinn Fein and the DUP are serial negotiators and under their stewardship, the Assembly will only ever be a place for brinkmanship and the politics of anger and sulk.
"Dysfunction will remain embedded in the structures because it is characteristic of the Hillsboro' politicians and part of their tactical armoury.
"For them, the structures are a means to an end, a stage in a process to which they are wedded, and in the meantime, it would appear, they will only ever endorse what suits their agenda and seek to obstruct the mandate of others.
"It is reminiscent of politics once underpinned by semtex, armalites and force.
"It would seem equally clear that in an attempt to appease the protagonists and keep them within this imperfect process, the government has agreed to side-deals.
"Sudden announcements on financial support for the promotion of the Irish language are hardly a coincidence.
"Statements by Gerry Adams this weekend at the Sinn Fein Party Conference seem to confirm as much.
"Martin McGuinness's earlier pronouncements on parades appear to suggest that the outcome of the considerations of the Committee to consider the issue is a foregone conclusion to which, presumably, the DUP has agreed.
"His party's affirmation of the Ruane Agenda begs the question as to the DUP's position on education and why they have left it to the UUP to insist that this, along with other issues, is dealt with now as part of any agreement.
"Clearly the government felt no need to include the UUP, or indeed, the SDLP for the process which produced the Hillsboro Agreement was anything but inclusive so the UUP is left, in the interests of its constituency, with no option other than to play by the rules laid down by those who were allowed to participate and put education and other equally important issues back on the table for resolution.
"To expect it to do otherwise and endorse a process to which it has had no input is unrealistic and displays a deep misunderstanding of the integrity and resolve of the UUP.
"Further, in failing to address education, such an obvious casualty of a dysfunctional Executive, the DUP in its haste and anxiety to agree a deal has disadvantaged hundreds of parents and children.
"This is what happens when your sole concern is your own retention of power.
"In the circumstances, the UUP has no choice other than to adopt its present position and policies with regard to the Hillsboro' Agreement and when these bring the success which is their aim, the country will have been well-served.
"The Minister of Education will have been made to face the reality that there is a sizeable constituency which does not endorse her actions or dismissive responses to those who seek compromise and the Stormont Executive will be functioning as a proper four-party coalition which shares responsibility and accountability, as originally envisaged and approved by the electorate.
"The Assembly will be in a better place to address the many issues, including Policing and Justice, by no means the most important, for health, employment and the economy are of greater concern to the electorate, for which it has a responsibility.
"If the UUP is listened too and its entirely constructive project acted upon, there will be stability, cohesion and greater opportunity for consensus."

Northern Ireland will be better served

"If as now seems likely the DUP having held its exclusive gatherings- wherever they have taken place, for few people seem to know - is now confident to the point to where it no longer needs the UUP, in spite of previous statements to the contrary, and caves in to the Sinn Fein-Woodward agreement, then not for the first time it will be failing unionism and linking itself inextricably to its new ally Martin McGuinness who in spite of his claims to be a 'problem-solver' chooses to eject people from his office and the process because he doesn't like the fact that their views differ from his own. Where now is equality and parity of esteem?"