Thomas Inskip was born at Clifton, Bristol, on 5 March 1876, the second son of James Inskip (1839-1909), a leading local solicitor, and the first son of his second wife, Constance Sophia Louisa. He was educated at Clifton College and at King's College, Cambridge, studying classics. He was called to the bar by the Inner Temple in 1899 and over the next decade developed a successful legal practice, taking silk in 1914. However, at the same time he was trying to develop a political career and stood unsuccessfully against Sir Edward Grey, the Foreign Secretary, at Berwick-on-Tweed in 1906 and January 1910.

On 30 July 1914 Inskip married Lady Augusta Helen Elizabeth Orr Ewing, eldest daughter of David Boyle, seventh Earl of Glasgow, and widow of Charles Orr Ewing, Unionist MP for Ayr Burghs. They had one son. During the First World War Inskip served in naval intelligence in London, becoming head of the naval law branch in 1918. He represented the Admiralty on the war crimes committee (1918-19) and successfully stood as the Conservative candidate for Bristol Central at the general election of 1918.

It was as a law officer that Inskip's political career developed. He became Solicitor-General in 1922 and in March 1928 succeeded Sir Douglas Hogg as Attorney-General. He lost his Bristol seat in the general election of 1929 but returned to Parliament in 1931 as MP for Fareham and became Solicitor-General in the National Government, then following the resignation of Sir William Jowett in 1932, became Attorney-General once again, remaining in that post until 1936, when he was appointed by Stanley Baldwin as Minister for the Co-ordination of Defence.

In this new post, Inskip played a significant role in resolving the long-running dispute between the Admiralty and the Air Ministry over the control of aircraft in naval operations. Eventually the Air Ministry was persuaded in July 1937 to accept what became the Fleet Air Arm. Inskip was also involved in the question of supply, initially opposing a separate Ministry, and also trying to establish a system of rationing between the services, while keeping expenditure within Treasury limits. In 1938 he was able to intervene to increase expenditure for the air force over Treasury objections and to maintain defence production at capacity. In January 1939, however, Chamberlain required him to resign.

Inskip was transferred to the Dominions Office in January 1939. In September of that year, on the outbreak of war, he was appointed Lord Chancellor in place of 1st Lord Maugham, as Viscount Caldecote of Bristol. In May 1940 he returned to the Dominions Office as leader of the House of Lords. In October 1940, however, his political career came to an end on his appointment as Lord Chief Justice, the first former Lord Chancellor to be appointed to the office. He remained in this position through the war, though towards its end his health deteriorated and he resigned in January 1946. He died at his home, Greystones, Enton Green, near Godalming, Surrey, on 11 October 1947.