Actually the Morioris from the Chathams were here first. Harsh tratment by the Maoris first and then the Europeans virtually saw them become extinct. The last full blooded Moriori "Tommy Solomon" died in the 1930's and todays survivors number several hundred, have a very severly diluted lineage.
Actually the British were asked by the Maori chiefs to step in because of fear of the French, and what the Maoris were doing to each other. They were actually slowly wiping each other out
Eg Ngapuhi chief Hongi who made a trip to England in 1820 to meet the King. On his return to New Zealand he stopped off in Australia and traded all the gifts the King had given him on 300 muskets and then initiated a ten year period of warfare and cannibalism on his fellow countrymen, slaughtering thousands for no apparent reason. Actually by the time the actual Treaty of Waitangi was signed in 1840 an estimated 60-80000 Maoris had died from inter tribal warfare
Here is an extract from the orginal 1831 letter by the Maori Chiefs, essentially asking for British help which eventually led to the Treaty of Waitang in 1840 which essentially laid out the rules for colonisation. and can be viewed in all its entirety by simply googling it.
... To KING WILLIAM, the gracious CHIEF OF ENGLAND.
King William,
We, the chiefs of New Zealand assembled at this place, called the Kerikeri, write to thee, for we hear that thou art the great chief of the other side of the water, since the many ships which come to our land are from thee.
We are a people without possessions. We have nothing but timber, flax, pork and potatoes, we sell these things however to your people then we see property of the Europeans. It is only thy land which is-liberal towards us. From thee also come the missionaries who teach us to believe on Jehovah God and on Jesus Christ His Son.
We have heard that the tribe of Marian* is at hand coming to take away our land, therefore we pray thee to become our friend and the guardian of these islands, lest the teazing of other tribes should come near us, and lest strangers should come and take away our land.
And if any of thy people should be troublesome and vicious towards us (for some persons who are living heree who have run away from the ships,) we pray thee to be angry with them that they may be obedient, lest the anger of the people of this land fall upon them.
This letter is from us, of the chiefs of the natives of New Zealand.
afterthought.
of course even the best intentioned plans do go astray and there was unscrupulous land grabs by the church, individuals and the government after the signing of the treaty.. However the NZ government has been making financial compensation to the disadvatanged tribes over the last two or so decades and it is still ongoing.