The Annual Register: World Events …. 1838 (1839). (1839). (n.p.): ProQuestrel.
The British Geological Survey seemed to miss this minor quake in their compiled list of earthquakes from the 18th and early 19th centuries that are featured in a post here: British Earthquakes from 1700 to 1849. I would suspect that was because the magnitude in the micro and minor range.
For more information on Georgian Earthquakes, there is also this lovely post: Reports of seismic activity in 18th century England – All Things Georgian