I would suggest checking the City of London Freemen's records - moved from the Corporation of London record office to the London Metropolitan Archives. The Freeman's records contain the apprenticeship indenture. Merchant Taylors apprenticeship records should be at the Guildhall. These records didn't record all family members but they do state who the father was of the apprentice and or freeman.
Abney Park cemetery (Bunhill was an earlier non-conformist cemetery) was very popular with non-conformists.
The oldest Arrowsmith burial at Abney Park is Adam aged 63 in 1850.
The National Archives have a Prerogative Court of Canterbury will for an Adam Arrowsmith.
Will of Adam Arrowsmith, Gentleman of Tottenham , Middlesex
Date 31 January 1851
Catalogue reference PROB 11/2125
There is an Adam Arrowsmith (age rounded down to 50) in Gravesend on the 1841 census with wife Mary (age rounded down to 40) neither born Kent.
Adam Arrowsmith married Mary Ann Averill at St Dunstan Stepney in 1840.
On the 1851 census Mary A. Arrowsmith aged 51 and born St Georges was living in Tottenham. She was a landed proprietress.
Looking at Abney Park Jeffryes' burials - and there are more than Arrowsmiths, I noticed Mary Temperance Jeffreys.
Temperance was a popular name amongst Arrowsmith marriages in Pallots marriage index.
Temperance Arrowsmith Thos Bennett 1800 Hackney, Middlesex
Temperance Arrowsmith Thos Beazley 1835 Hackney St John
Hackney marriages ususally don't appear on the IGI.
No marriage on Pallots for James Jeffryes and Mary Temperance ...... There is however a Jeffryes PCC will in Spitalfields at TNA.
Will of John Jeffryes, Cooper of Spitalfields , Middlesex 29 September 1834 PROB 11/1836
If any PCC wills prove usefully the beneficiaries can be tracked through the Death Duty registers at TNA.
As I don't know which Arrowsmiths and which Jeffryes you are interested in, so I can only speculate on possibilities.
Regards
Valda