Not clear who he is, but in Venn this might relate
Adm. pens. (age 17) at PETERHOUSE, Aug. 12, 1793. Of Essex. Probably migrated to Oxford and matric. (Wadham College) Nov. 4, 1795, ‘age 19; s. of John Thompson, gent., of Little Bursted, Essex’; B.A. (Oxford) 1799. Probably C. of Stowmarket, Suffolk. Died Dec. 5, 1835, aged 58. The suggested identification in T. A. Walker, 365, with the R. of Pentlow, Essex, is incorrect; see John Bull, of Christ's (1785). (T. A. Walker, 365; Al. Oxon.; G. Mag., 1836, I. 210, where he occurs as ‘John Bull, B.A.’)
In Foster:
either s of John of Cubley, co. Derby pleb; St Ed Hall, mat 14/3/1798, aged 20; BA 1801, <MA 1809
or
S John Thompson of Little Bursted Essex, arm; Wadham mat 4/11/1795 aged 19; BA 1799
Fact is an MA (1683) of same name might encourage former identity? Or is he a lit.?