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He entered a small mark at Goldsmiths Hall in 1828 in an unspecified category from 10 Castle Street, Leicester Square.
The 1841 UK Census suggests he was born around 1782. The record shows he was born in England but not in London and was working as a silversmith at 70 Castle Street, Soho.
The 1843 Post Office Directory continued to record him in the same trade at the same address.
He was named as a silversmith in the record of his daughter’s marriage in 1848 but is not shown as a witness.
No further information has been found for him.
It may be coincidence that a Charles Kelk was christened the son of Charles at St Peter Cathedral, Sheffield in 1782 and that Charles Kelk the elder may have been the same to have entered a maker’s mark at the Sheffield Assay Office in 1775.

A Charles Kelk, Plater, Pinfold St Birmingham is noted in Wrightsons Triennial Directory for 1815. A Chares Kelk noted as formerly of Birmingham and late of "Burley" St Strand, Silver Plater is recorded as a bankrupt in the London Gazette, 16th June 1821.

Thank you for the further information.
London Land Tax records, recently available on website, show that his address was Burleigh Street
from 1818-28 and Castle Street from 1828.
As he required a maker's mark at Goldsmiths Hall in 1828 the 1821 bankruptcy seems not to have caused him permanent harm.

Mike