O'Connor was born in Ranchi, Jharkhand, British India. He was the second child of the Revd. William O'Connor and Emma (née Kennedy).
O'Connor was educated at Saint Columba's College, Dublin where he was a chorister and cricketer. From here he won a choral scholarship to Worcester College, Oxford but was unable to take it up due to the First World War.
In 1915, he joined the Indian Army as an officer in the 14th (KGO) Ferozepore Sikhs. He was awarded the Military Cross "for distinguished and meritorious services" at the Battle of Sharqat, during the campaign in Mesopotamia against the Turks. Sir Kenneth later wrote a short account of the Battle of Sharqat. After the war he left the Indian Army with the rank of captain, though he was later made an honorary colonel.
O'Connor then joined the Foreign & Political Department of the Government of India, serving as the British District Commissioner in Charsadda, a district of Northern India (now Pakistan) adjoining the Khyber Pass.
In 1922, he resigned and returned to England, where he was called to the London Bar in 1924 by Gray's Inn.
After a short time practising at the London Bar, he became a partner in the firm of Drew & Napier in Singapore. In Singapore, he met and married Margaret Helen Wise, the eldest daughter of the rubber planter Percy Furlong Wise, of the Devonshire dynasty.
As Chairman of the Straits Settlements Association, O'Connor played a key role in planning the civilian evacuation of the island in the event of a Japanese invasion. He escaped from Singapore in a small, open sailing boat with unsuitable sails and a children's atlas for navigation. Despite these impediments, with three others, he successfully sailed to Sumatra. O'Connor later wrote a short account of this adventure, entitled Four Men in a Boat. He had already evacuated his young family (Anthony, born 1933 and Hugh, born 1940) to Australia, where he later joined them.
In 1943, having joined the Colonial Legal Service, O'Connor was appointed Attorney General of Nyasaland (now Malawi). After the war he returned to Singapore to reconstruct the legal practice of Drew & Napier. In 1946, he was appointed Attorney General of the Malayan Union and in 1948, Attorney General of Kenya.
In 1951, O'Connor was appointed Chief Justice of Jamaica in which position he served until 1954. In 1954, he was recalled to Kenya as Chief Justice, serving until 1957.
At this time, the Mau Mau Uprising was at its peak. O'Connor was the senior presiding judge in many Mau Mau trials, the most notable being that of Dedan Kimathi, whom O'Connor sentenced to death in 1957.
O'Connor finished his legal career as President of the Court of Appeal for Eastern Africa from 1957-1962, with jurisdiction over Kenya, Uganda and Tanganyika.
Following independence, Sir Kenneth and Lady O'Connor retired to their house, Buckland Court, in Surrey, England in 1962.
Sir Kenneth died on 13 January 1985, aged 88.