Thanks everyone for your interest and help. James Oatway was born in 1814 in Shirwell, near Pilton, Devon. He married Eliza Mattingley in 1837 in Pangbourne, Berks. They had Harriet and then moved to London. He was a basketmaker. Eliza did die in 1851. James's father was a weaver living in Pilton called John.
I had no idea that he had married Ann Thorpe in Stepney (Thanks Nigel). Baby Alice of Whitechaple, as posted by Monica, might have been their child. So if Ann died in 1854 that means that James married Elizabeth Tarrant from 1855.
I really don't know about the Tarrants of Marylebone as the only references Elizabeth uses on the censuses are that she come from Lime Street, City of London.
I don't think that the Jamaica Fields James Oatway is connected.
Best wishes,
Oatway