Looks like I've managed to crack it - found other documents which show it more clearly as West Sleekburn - just near Newbiggin after all. Thanks for everyone's help, though, Andy's efforts being particularly valiant.
Am having to go on censuses as family memory only reliably takes us back to my great grandparents, on the whole. Yes, I'm on ancestry.co.uk - seems like the thing to be on. Have found Genes Reunited to be decent though - found two obsessives who saved me Christ knows how much work

Not much cop if no one shares any ties, though, no.
Ireland is even harder than Scotland thanks to the arsonists of the Easter Rising - if only they'd known their place, genealogists would've been saved a lot of hassle...
What does your work account give you access to? Just national censuses and such, or do you get other records like local death inquests and marriage certificates? That could come in handy, mate.