In 1786 he travelled to England in order to search for documents relating to mediaeval Danish-English contacts. In 1787 he hired British Museum employee James Matthews  to transcribe the sole extant manuscript of the Old English epic poem Beowulf and made another copy himself. Under a commission from the Danish government, Thorkelin had prepared Beowulf for publication by 1807. Unfortunately during the Battle of Copenhagen (1807) his house was burned, and the manuscript of his edition (the work of 20 years) was lost. The two transcripts survived, however, and Thorkelin began all over again. The poem was eventually published in 1815.  Thorkelin was also the first scholar to make a full translation of the poem.
The Thorkelín transcriptions are now an important textual source for Beowulf, as the original manuscript's margins have suffered from deterioration during the 19th and 20th centuries. His early copies provide a record in many areas where the text would otherwise be lost forever.
Thorkelín is generally regarded as one of the pioneering figures in Nordic and Germanic studies. Moreover, his visit to Britain reinvigorated interest and appreciation in the island's Germanic past, in ways both scholarly and Romantic. However, this view is not without its detractors; Magnús Fjalldal describes Thorkelín as "essentially a fraud as a scholar" and lists a number of errors in Thorkelín's edition and translation, many of which were pointed out by contemporary reviewers.
G. J. Thorkelín, De Danorum rebus gestis secul. III & IV : Poëma Danicum dialecto Anglosaxonica : ex Bibliotheca Cottoniana Musaei Britannici / edidit versione lat. et indicibus auxit Grim. Johnson Thorkelin, 1815.