Hi Humphrey,
When you get time a search on
http://www.london-gazette.co.uk/search brings up many entries.
We know that Charles the Mayor was an architect and banker (his father was a carpenter and joiner and I have never seen any mention of him being involved in the banking business).
A piece in the London Gazette on 12 September 1844 mentions Charles Humfrey and Charles Humfrey junior carrying on the business of bankers at Cambridge.
15 Nov 1844 a partnership in an oil and candle business is dissolved between Charles Humfrey and another person. They traded as E. Manning and Co.
31 July 1848, 19 September and 17 October 1848 references to Charles Humfrey the younger, late of Cambridge, banker and of Manor-street, Camberwell and mentions Manning and Co.
5 December 1848 and 12 January 1849 mention Charles Humfrey the elder, late of Cambridge, banker, deceased.
There are many more later mentions of Charles and a Charles junior/the younger who relate to Charles (1808) and Charles (1834) to do with oil/candle type businesses.
So from the above we have Charles the Mayor and his son involved in the Cambridge Bank in 1844. Around that time or just before the Cambridge business or Humfrey was in serious financial trouble.
From the next we know learn that Charles the younger and late of Cambridge, banker was in Camberwell and in the oil and candle trade.
And in 1848 Charles Humfrey is described as the elder and late of Cambridge.
The articles then show a move to Chester.
We also know from census records that Charles (1808) was living in Camberwell in 1851 and 1861 and was in the oil and candle business and Charles (1834) was in Newington in 1861 also in the oil trade.
So to my mind the connection is pretty clear.
Selina