Having shown an unusual aptitude for languages, Coggan was awarded an open exhibition to St John's College, Cambridge. He entered St John's College in 1928 with an open exhibition, but he was so studious that it was later upgraded to a full scholarship. He was outstanding in oriental languages, Hebrew, Aramaic, and Syriac, and won a first in both parts of the Tripos examinations in 1930 and 1931. He won the Tyrwhitt Hebrew Scholarship, the Mason Hebrew Prize, and the Jeremie Septuagint Prize.