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He may have been the son of John Pearson, a mathematical instrument maker and his wife Sophia of Borough, Southwark, christened at St Mary Lambeth in 1790 and who signed indentures in 1804 to be the apprentice of John Samuel Reily. Reily traded as a goldsmith in Gutter Lane but was free of the Fishmongers Company.
This George Pearson was made free in 1811-12.
A mark was entered at Goldsmiths Hall in 1817 by a small worker of this name from 104 Dorset Court, Fleet Street.
No later information has been found.

Should it help, here are some details of John Pearson, the mathematical instrument maker:

Noted at:
City Road, London - 1793
6, City Road, London - 1805
Lambeth Walk, London - 1812

He was free of the Stationers' Company in 1782 and served his apprenticeship under William Evans (I), who was also free of the Stationers.

I have details of only one son, John (II), who started an apprenticeship in 1812 under the Armourers' and Brasiers' Company of London.