Jenkins' real name was John Roberts (or John Cocking? See below). He assumed the name Robert Jenkins when he came to Wellington.
Roberts/Jenkins had arrived at Sydney from England in 1835 with his wife, 11 daughters and two sons and settled at Boro Creek, Murray, NSW. He then left his family and came to Wellington in early December 1839 with his eldest son. Shortly after he is said to have bought a barrel of beer and set it up in a hut on the Thorndon beach, creating one of Wellington's first drinking spots. Later on he was the first owner of the New Zealander hotel in Manners St.
Jenkins was one of the aldermen elected to the first Wellington council in 1842. He branched out into transport, stock dealing and farming. In 1841 he leased 100 acres of hill pasture in Hataitai, which he used for horse-breeding. This land became known as Jenkins Estate and was bought for development by the Hataitai Land Company in 1901. Jenkins was a keen supporter of horse racing and was prominent at the first race meeting in Petone in October 1842.
Edward Jerningham Wakefield, writing about 1844, described Jenkins - "Old Jenkins, as he is generally called, is quite a character. He can suit his conversation and manners to any class of society ... although of unknown origin and ignorant even of writing, he has many sterling qualities."
Jenkins died in Wellington on 23 November 1859, leaving a family of adult children in Australia as well as three children born to his partner E Hiri (or E Hui?) in Wellington.
Sources:
The City of the Strait, other books.
Sale of Jenkins Estate, New Zealand Times, 7 June 1901
Probate of Robert Jenkins, Archives New Zealand ref AAOM Series 6029/3/128 Item code R22206974
Colourful story of the early days at Lower Boro, Braidwood Dispatch and Mining Journal, 9 Jul 1943 http://nla.gov.au/nla.news-article119257310
John Cocking?: http://www.familytreecircles.com/looking-for-the-family-of-robert-jenkins-of-wellington-new-zealand-49907.html