Hi
With a city the size of London (the largest city in the world with a population of just under 1 million in 1812), which was a very fluid population - people arriving into the city on a daily basis and an extremely common surname like Green - there are going to be a great many William Greens in the London area (on the 1841 census in the county of Middlesex and the City of London there were 300 on that night 8 of whom were in Holborn).
Without further evidence that Edward Richard Frederick Green's parents actually came from London let alone were born in Holborn parish you can't really be sure of tracing William Greens back in that parish and know they are connected.
The metropolitan borough of Holborn (one of 28 London boroughs and the smallest) was created from the parish of Holborn and some surrounding parishes in the 1880s. It was estimated to have over 80,000 people living in that area in 1812.
http://en.wikipedia.org/wiki/Metropolitan_Borough_of_HolbornYou really need to come forward first with as much information on Edward Richard Frederick Green as possible to find as much information as you can about his father. Was his occupation a jeweller? Do you know of any other siblings? If possible it is crucial to try and find William's burial date, or if he lived into his 50s his death registration to ascertain his age and therefore have some more solid evidence for his approximate birth year. If he did live to an older age have you found him on a census or have some possibilities for his burial?
The William Green who was a jeweller on the 1841 census.
1841 census HO107 670/2 folio 11
Baldwin Gardens St Andrew Holborn
William Green 50 Jeweller
N K Green 50
Mary Green 24 Book folder
Martha Green 19 Bookfolder
all born in county (though the answer yes to this question on the 1841 census can be unreliable). Adult ages, those over 15, are usually rounded down to the nearest 5 on the 1841 census.
'Edward Richard Frederick' was living at No 6 Tennis Court Holborn on the 1841 census HO107 670/11 folio 23, a cabinet maker. Who registered his death in 1848?
Not necessarily the same man as the William in 1841
1851 census HO107 1540 folio 4?
41 Liquor Pond Street Holborn
William Green 58 Head Widower Artist in Gold London
Mary A Green 29 Daughter London
Have you found 'Edward Richard Frederick's marriage? Who were the witnesses? Does it help to confirm a connection with the William who was a jeweller?
Regards
Valda