Atkin attended Christ College, Brecon and won a demyship to Magdalen College, Oxford where he read classics and literae humaniores, enjoying playing tennis in his leisure time. Atkin was called to the bar by Gray's Inn in 1891 and scoured the London law courts assessing the quality of the advocates so as to decide where to apply for pupillage. He was ultimately impressed by Thomas Scrutton and became his pupil, joining fellow pupils Frank MacKinnon, a future Lord Justice of Appeal, and Robert Wright, another future Law Lord. He took chambers at 3 Pump Court but, as did most beginning barristers at the time, struggled to find work. He shared living accommodation with Arthur Hughes who later married Mary Vivian Hughes whose book A London Family 1870-1900 mentions Atkin. He eventually established a practice in commercial law, in particular in work on behalf of the London Stock Exchange, and became known as a subtle advocate with no need to rely on theatrical effects. His practice grew from about 1900 and made a favourable impression when appearing before future Prime Minister of the United Kingdom H. H. Asquith who was sitting as an arbitrator. Asquith was so impressed that he secured a pupillage for his own son Raymond at Atkin's chambers. By 1906, The Times considered him probably the busiest junior at the Bar. In that year Atkin took silk. Once John Hamilton was made a judge in 1909 and Scrutton in 1910, Atkin dominated the commercial Bar.
Atkin became a Lord Justice of Appeal in 1919. In the 1920 case of Meering v. Graham-White Aviation Co. Ltd Atkin showed his disapproval of unjustified restriction on civil liberties by holding (obiter) that a person could sue for false imprisonment even under circumstances where he had been unaware of his imprisonment at the time. Again in 1920, in Everett v. Griffiths Atkin held that Everett was owed a duty of care by a Board of Guardians who had detained him as insane on inadequate grounds. However, Lord Justices Scrutton and Bankes held otherwise and their majority prevailed over Atkin's dissenting judgment.
From 1928 until his death he was a Lord of Appeal in Ordinary under the title Baron Atkin, of Aberdovey in the County of Merionethshire. Atkin was strongly motivated by his Christian faith and relied on testing the law against the demands of common sense and the interests of the ordinary working man. He came to a settled view early on in hearing a case and, as a Law Lord, his colleagues often found him indefatigable in his opinions and difficult to persuade as to the merits of alternative views.
The couple had six daughters and two sons, the elder son being killed in World War I. Atkin's daughter Rosaline became a barrister of Gray's Inn. The fourth daughter, Nancy, to her father's delight, became an actress. Nancy made her debut in Liverpool and was discovered and brought to London by Charles Hawtrey and A. A. Milne. Atkin's grandson, by his daughter Lucy Atkin, was the politician and business leader Sir Toby Low, 1st Baron Aldington.
Atkin enjoyed the music hall and in particular the humour of George Robey and Marie Lloyd. He and his wife were fond of entertaining at their succession of town homes in Kensington with musical evenings. In 1912 Atkin realised his ambition of buying a house Craig-y-Don in Aberdovey and from that time, he spent every summer there with his family. At Aberdovey, Atkin enjoyed tennis, golf and bridge. He was an enthusiast for the literary works of Edgar Wallace. Atkin was popular with the community in Aberdovey and was paraded into the village on a hand-drawn cab on his appointment to the High Court. When possible, he sat as a Justice of the Peace in Towyn and Machynlleth, and eventually chaired Merionethshire Quarter Sessions.
He died of bronchitis in Aberdyfi where he was buried.