Convocation devised its internal political arrangements in the months after its inauguration. The Charter of 1858 had provided that the Chairman should be elected for three years, and would be eligible for re-election. Convocation decided to elect its Clerk every year. In addition there was to be an elected Annual Committee, initially with thirty-two members, but enlarged in 1862 by the addition, ex officio, of any member of Convocation who was a Fellow. In 1862 this meant only seven additional, ex officio, members, but from the end of the 1880s onwards there were never less than twenty. From its inception until 1896, the thirty-two elected members of the Annual Committee were chosen by two groups of graduates – sixteen from those with degrees in Arts and Laws, and sixteen from those qualified in Medicine and Science: but the Science graduates only came on the scene in 1865. The two groups of sixteen operated as sub-committees to deal with most of the affairs of Convocation. From 1896, the title was changed from Annual to Standing Committee, and its total elected membership was increased to thirty-six, nine from each of the Faculties of Arts, Laws, Medicine and Science.

Any member of Convocation could be nominated to serve as Chairman, as Clerk, or to sit on the Annual Committee, but the choice from among those nominated was made only by the members present at the May meeting of Convocation.

Though there were four Chairmen and three Clerks during the years from 1858 to 1900, there were only two contested elections. In 1864 John Storrar became Chairman by defeating James Walter Smith: the voting was 121 to forty-two. In 1876, Henry Ebenezer Allen beat Talfourd Ely by two votes – 108 to 106 – to become Clerk. Once in office, no Chairman or Clerk was ever challenged when re-nomination was needed.

There was more competition for places on the Annual Committee, but in most years it was on a small scale. In 1859 and 1860, the nomination of exactly thirty-two candidates was moved on each occasion by Francis Sibson, and accepted without question. In time for the election of 1861, a Standing Order had been adopted whereby nominations should be made by five or more members. This procedure produced exactly sixteen medical men and seventeen graduates in Arts and Laws, nominated as a group by six members, all of whom were among the nominees.