Thank you Rena, your thoughts certainly make sense and thank you to Jorose for the site you've mentioned. I hope the following isn't over the top but it may give you an idea of where I'm coming from.
These are all I can find in the censuses.
A family in Tower Hamlets, Whitechapel
Barnet born 1865-1868 Cracow, Austria
Rachel born 1863 Cracow, Austria
Hyman born 1888 London, Spitalfields
Solomon born 1895 London, Spitalfields
In Cheetham, Manchester
John born 1837 Cracow, Austria
All the above are Silverfield which appears to be an English form of Silberfeld
Leeds, Yorkshire
Henry Silberfeld born 1856 Cracow, Poland
I knew nothing of the history of Krakow until I did a search. It appears that the 1700’s were very turbulent as Russia and Prussia tried, and failed twice, to annexe Poland between them. In 1795 Austria joined in and succeeded in splitting Poland three ways. Krakow was in the Austrian segment, which came to be known as Galizia. Anti-Semitism kicked in with a vengence and Jews were stripped of their businesses, in effect preventing them from earning a living. In 1799 a law was passed to prevent Jews from selling property to non-Christians. This would mean that they would become homeless if they did and they may not have had any choice if they were being vandalised to force the issue. Many left Krakow and emigrated via Amsterdam and Hamburg but most Silverfields/Silberfelds crossed the Atlantic to America. I have only ever found six in all the British censuses and four came from Krakow.
My GGG Grandmother was Alice Silverfield. I only learned of her surname from a birth cerificate for her youngest son David Grundy. I couldn’t get my GG Grandfather’s certificate because he was born about 1830. From all the evidence I have gathered, Alice claims to have been born in Astley, Lancashire in 1804 (give or take two years) making her the earliest Silverfield I can find. She was supposed to have been married to David Grundy born Astley, 1798, but no marriage for them has ever been found. He was a canal boatman and they lived on the boat until they eventually got a house in Plank Lane, Westleigh, Wigan. David continued as a boatman along with at least two of the kids. The OPC site for Lancashire has extensive Christian BMD transcriptions for the entire county but not a single Silverfield, Silberfeld or anything like it, can be found. David Grundy shows up. Further, of their seven children only the two youngest appear to be baptised. Was Alice really born in Astley or was it convenient to say so in the censuses because her husband was. My thoughts are that if she was of Jewish parentage and escaped from Krakow she could well have been suspicious of an authoritative figure such as a census enumerator. The canal connects with Manchester where the Great Synagogue was built in 1806. I found this on the internet. Prior to that a building was rented but before even that from about 1740 services were held in an alley that became known as Synagogue Passage. I hope you don't think me stupid but Alice has really caught my imagination with such an odd name.