Andrew,
The Whiteheads of Farnley are my mother's family. This particular Julius (1) was my great grandfather's brother, so not in a direct line, but he is interesting for other reasons. He was born about 1838, probably at Moor Top, Farnley.
His father is another Julius, (2) born about 1799 in Farnley, married Jane Holdsworth in 1826 at Leeds Parish Church (St. Peter's). He was a farmer.
His father seems to have been yet another Julius, (3) born about 1755 also in Farnley, married Martha Huddlestone of Stanningley in 1797. His father does seem to have been called John, but I know no more about him yet. Julius (3) was 42 when they married, so this could have been a second marriage. I have been unable to trace a first one, though.
I know the dates seem incredibly far apart, but Martha was still living at the time of the 1851 census, described as Julius (2)'s mother!
Family legend has it that the Whiteheads had lived in Farnley since at least the 1650s, the evidence being a large pewter plate stamped I W M (for John and Mary Whitehead) 1654 on the rim. I have seen it, it used to hang over my grandmother's mantelpiece.
There seem to have been an incredible number of Juliuses (Julii?). There's another one in Tong in the 1820s, (if you don't know the area that is probably nearer Moor Top than Moor Top is to Farnley), and also another one in 1762, also in Tong.
In addition, there was a Whitehead family living at Quarry Hill, Leeds, and maybe another Whitehead family in the town somewhere.
Sadly, I haven't come across any in Morley or Churwell, but I'm sure it's only a matter of time.
Hope this helps, and good luck in your hunting.
Jon