On the 1891 census, there is a Murphy family living at High Street, Barton Upon Humber, Barton-On-Humber as follows:
Matthew born 1850 in Ireland, plumber and Lead Burner
Sarah born 1855 in Garton, Yorkshire
Hy Jon (but looks a bit like Jas on census) born 1883, Barton, Lincolnshire
Jno W born 1885, Barton, Lincolnshire
Mary E born 1890, Barton, Lincolnshire.
So from that I guess Henry James' father was called Matthew.
Lizzie