How high up the slopes are the two faults? Are they around the high and low troughs marked on o.s.
Has cat hole been dye tested to long kin west etc.
If Jenkins beck (rises) takes the water between the faults that’s quite significant.
I think the strip of limestone SW of the NCF is quite narrow. Have a look at this geological mapping tool: https://mapapps.bgs.ac.uk/geologyofbritain/home.html
It would appear that the NCF passes through Jenkin Beck SW of the rising of interest.
High & Low Troughs are clearly fault guided but they're a long way above (NE of) the NCF.
(Incidentally they may be a continuation of the Clapdale Fault further to the SE.) There is at least one other fault between High & Low Troughs, running at an angle to them.
At Ingleton the NCF crosses the road just to the SW of Skirwith Cave; at Clapham it passes through the head of the lake in the Nature Trail.
In the area of Blindfield Well above Cold Cotes the NCF runs pretty much along the back road.
Beware of using that mapping tool; it can be quite absorbing (i.e. time consuming!).
Although it's highly likely they're hydrologically connected, I'm not aware of any test from LKW where tracer was picked up at Cat Hole. The test would have to be timed well and would probably involve getting a right soaking en route up to LKW.