This will be them in 1851 census, if you don't have it.
Whitesmiths Buildings, Hawkdale,
James Murphey, 52, Teacher of

(Could be Art and Mathematics?), b. Ireland,
Hannah ", wife, 45, b. Cumberland, Walton (?),
Christopher ", son, 8, b. Cumberland, Dalston,
Edward ", son, 5, b. Cumberland, Hesket in the Forest,
HO107/2431/321/1
And in 1841.
Lintongill, Ivegill, Dalston.
James Murphy, 40, Farmer, b. Ireland. (could be an S, but looks more like an I).
Hannah ", 35, b. Cumberland,
Ruth ", 10, b. Cumberland,
John ", 8, b. Cumberland,
William ", 3, b. Cumberland,
Frances ", 1, b. Cumberland,
HO107/164/23/5/4
Familysearch has his baptism 3 Aug 1845, Ivegill / Highhead, Edward Murphy son of James and Hannah. Doesn't seen to be a corresponding birth record on GRO, but registration was not compulsory. Some of the other Murphy/Walker siblings are on the GRO.
Alan.