Cable head is too small when I came to change the shifting (gear) cable on my claude butler bike I found that the original cable has a slightly bigger head(nipple) than the replacement cables I have-3.9mm compared to 3.5mm and consequently will not work-wtf
The mech is shimano v brake
Sounds to me like you've got Campagnolo-sized shifter ends.  The difference is subtle but definite.
Left is Shimano, Right is Campagnolo.
Not sure how you're measuring, using a ruler might explain the difference. The common-quoted diameters are
Shimano shifter end barrel diameter: 0.173&quot; (4.39 mm)
Campag shifter end barrel diameter:  0.159&quot; (4.04 mm)

Generally speaking, campagnolo stuff is more expensive because it is less common, because it is more expensive (loop!)  These shouldn't cost more than a couple of dollars each.