I made several additions to the above post, but then hit its length limit, so here they are separately:
EDIT: And one more update from me: familysearch.org has several records suggesting a Robert Cecil Radmore, born 13 September 1895 in Dalston, Hackney, London, and still living there at the age of 16 in 1911. During World War I, it has him serving in the Honourable Artillery Company, 4085 Regiment, 1st Reserve, 2nd Battalion in 1915, and registering for the draft in 1942, now in New York City.
Separately, there are records for a Robert Radmore (born England), married to Mary (born Ireland) and with son Peter (born New York), listing Robert and Mary as emigrated to the US in 1926, and the whole family as resident in Manhattan (Districts 0501-0750) in 1930, then with a six year old daughter Mary (also born New York) and living in Assembly District 14, Manhattan in 1940.
EDIT 2: Aha -- and going back to libertyellisfoundation.org, there's record of a Robert C P and Mary C Radmore arriving in the USA on the Ascania in 1926...
EDIT 3: And going back to jeffseeley.org, I note that he has Robert Radmore and Mary Gorman as having two children, Peter and an unnamed female child who married a John D. Foster, deceased 2002 in Chicago. The Chicago Tribune has a John D. Foster, married around 1966 to Adrian Radmore Foster:
http://articles.chicagotribune.com/2002-07-15/news/0207150017_1_mr-foster-montgomery-ward-longtime-wardsSlightly curious, but there are several other records of a Mrs. Adrian Radmore Foster in Chicago, so it's most likely correct. Adrian can, it seems, also be a girl's name (not just Adrienne, Adrianne, or Adriana); perhaps she was Mary Adrian Radmore, and goes by her middle name as it seems her mother did? There are several records on Google of a Mary Adrian Foster.
EDIT 4: And returning to familysearch.org, there's a Mary Adrian Radmore arriving in New York in 1953, on the Sadena.
EDIT 5: I'm familiar with the other ship names above, but had never heard of the Sadena, so I went back to the Liberty Ellis Foundation and looked at the manifest. There was indeed a Mary Adrian Radmore listed on board, but it wasn't a ship -- it was a plane. Specifically, it was TWA Flight 953 from Shannon, Ireland to New York, arriving 10:13AM on September 2nd, 1953 in New York.
That flight, incidentally, was on N6020C, a Lockheed Constellation L-749A that was just 2.5 years old at the time, and a little under 14 years later would serve TWA's very last passenger-carrying Constellation flight in April or May 1967. Why they have her listed as Sadena I don't know; her name was actually Star of Kentucky. That exact plane can be seen in the French-language film Escale a Orly (
http://www.impdb.org/index.php?title=Escale_%C3%A0_Orly), and there are lots of photos of her on the web.