[See also 'English Jewish surnames revisited'.]
My late father had a special interest in Jewish history and a very positive attitude towards Jews (unlike his brother whose belief in an international Jewish conspiracy was unshakable).
My paternal grandparents and great-grandparents were either Roman Catholics or members of the Church of England and there was no suggestion of any awareness of Jewish ancestry. But, oddly, virtually all my father's friends were either Jewish (surnames: Pittman, Babel, Mossenson ...) or had surnames which are often indicative of Jewish ancestry (Miller, Bloomfield, Rees ...).
Even his barber was Jewish (of German origin) and, when Dad retired due to ill health, the hairdresser (whose shop was near his office) gave him a card with a touching note in which he referred to himself as my father's "devoted Freund."
I never talked to my father about these matters as I only began to take an interest in them after his death. Was he aware of the possibility of Jewish ancestry? Perhaps. Did his Jewish friends suspect that his family was Jewish or part Jewish? This is very possible. In an early photograph my rather anti-Semitic uncle bears an uncanny resemblance to Franz Kafka!
In fact there are surnames in my family tree, mainly on my father's side, which do suggest Jewish origins. Beck, Fisher and Langman, for example.
English names have been adopted by Jewish immigrants over the centuries. The migrations of the 19th and 20th centuries are well known. Earlier waves of Jewish immigration are less well documented. Many descendants of Sephardic Jews from the Iberian peninsula settled in the British Isles in the 16th and 17th centuries and gradually assimilated into the Christian mainstream.
Amongst the names of my forebears which I am looking at in this regard in addition to the names mentioned above are Davis, Lester, Harris, Michell, Moyse; and also English, Pember, Russell, Sturgeon and Ward.
I am not just relying on names, however. Family stories also give some support to the idea of Jewish connections.