Sorry for the delay – for some reason I didn’t get a notification of your reply.
In the 1901 census Elizabeth and her father were living at Cocklaw Fulling Mill, a couple of miles north of Wall (just south of Chollerton). If you look at this old map of the area https://maps.nls.uk/view/102346452#zoom=6&lat=8253&lon=6799&layers=BT you will see that this is named as Cocklaw Walk Mill (Fulling).
So I think the answer is that the word you have read as Wark on the certificate is actually WALK.
You can see the exact location on a current Ordnance Survey map here https://historicengland.org.uk/listing/the-list/map-search?clearresults=true and entering the number 1156625
I hope this is helpful
Jennifer Britton