On 22 November 1979, on BBC1, Jenkins gave that year's Dimbleby Lecture, entitled Home thoughts from abroad, in which he argued for a realignment of British politics and a new centre party.

From the beginning, Jenkins was the prime mover behind the formation of the Social Democratic Party (SDP) together with three Labour politicians usually credited with founding the SDP—David Owen, Bill Rodgers, and Shirley Williams. Preparations for launching the new party grew more explicit—as reflected, for example, in Jenkins's follow-up speech to the parliamentary press gallery on 9 June 1980 and then on 1 August 1980 Owen, Rodgers, and Williams (or the 'gang of three') published a manifesto as an 'open letter' in both the Daily Mirror and The Guardian. It was a development that took place without reference to Jenkins, but he, perhaps more than anyone else, realized its significance.

That autumn Jenkins was involved in a succession of meetings with Owen, Rodgers and Williams, not without disagreements. David Owen did not believe in Jenkins' particular vision of a centre party and also thought that the leader of the party should be its most popular member, Shirley Williams. The 'gang of four' coalesced, however, and the day after Labour's special conference in January 1981 they announced the formation of a Council for Social Democracy.

The Social Democratic Party was formally launched in London on 26 March 1981 with fourteen former Labour MPs and a former Conservative MP. Jenkins attempted to get back into Parliament first in a by-election in the safe Labour seat of Warrington in July 1981 and then (successfully) at Glasgow Hillhead in March 1982 (the SDP was by this point allied with the Liberal Party in the SDP Liberal Alliance). In June the party membership voted Jenkins in as the party's first leader.

In the summer of 1982 Jenkins retired from the party leadership in favour of David Owen. The SDP fought the 1983 general election as the Alliance and although Jenkins retained his seat at Glasgow Hillhead, it was a poor result overall. The SDP dropped from twenty nine to six seats in the Commons alongside seventeen seats for David Steel's Liberals.

The years after the general election began Jenkins' withdrawal from front-line politics. When the SDP moved towards a merger with the Liberals—supported by Jenkins but opposed by Owen—the gulf between Jenkins and Owen widened. In the 1987 general election, Jenkins lost Hillhead (to George Galloway, Labour) and took the majority of the SDP into a merger with the Liberal Party (initially called the Social and Liberal Democrats, but from 1989 the Liberal Democrats) while David Owen lead 'the continuing SDP' party, which survived barely three years.

[Adapted from the Oxford Dictionary of National Biography article on Roy Jenkins].