I have discovered that my great grandmother was born Elizabeth Cain. She married James Holford in Bethnal Green, London in 1862. On the marriage certificate her father is named as John Caine, mariner (the spelling seems to vary but she was illiterate, placing her mark on her marriage certificate). In the censuses of 1871, 81 and 91 her place of birth is far from consistent - various different parts of London which appears to be the case with many who migrated to London. They were also married using his parents' address suggesting that her parents were not in London.
The 1861 census only identifies one John Cain who is a mariner. He lives on Bridge Street, Peel. Elizabeth was born between April 1838 and September 1838 (deduced from date of census and date of death). The only Elizabeth Cain in the 1861 census in Britain who seems to fit is a servant to Esther Cain (annuitant) in Rockmount Road, Peel.
Can anybody help? I know that people can be missing from census transcripts and that it is possible that there is no IoM link. But if anybody knows of an Elizabeth who left for London it would be very appreciated.