Arthur b 4-2-1886 Birmingham Lillian Clara b 4-19-1885 Birmingham Majorie W b Eng c 1912 William Arthur b 7-15-1915 Springfield; m Eleanor; d 3-23-1980 Quincy; served Korean War 10-23-1850 to 8-15-1952; 1943 worked Charlestown Navy Yard. Dorothy A b c 1917 MA both girls still at home 1943. 12-6-1919 Lillian, and all 3 ch went to Eng to visit her parents; they returned 6-21-1920.Lillian states Arthur left Eng 4-3-1913 [also on NY Passenger List], and was naturalized 9-9-1918 Springfield MA.
Lillian made another trip to UK in 1951 Arthur has been a paperhanger, machine operator for Westinghouse, and a painter [per census]
Arthur was alone on ship, so sent for Lillian & Marjorie later, but I didn't find her.She IS listed on UK Departures, but I don't have access.
If you need the parents, and know when Arthur and Lillian died, their death certs and/or obits might be of help. I didn't find marriages for the 2 girls.
Also try the ENGLAND forum for lookup for 1901/1911 census. When Arthur left Eng he resided Balsall Heath, Birmingham, Worcestershire.I didn't find any info from FREE B/M/D for the UK.