Yorkshire is one of the largest counties. Suggest you try the Yorkshire list Rebecca or even Cumbria ,Westmorland is part of Cumbria now and is bordered by Yorkshire, Lancashire etc.so if there is not a Cumbria list West Yorkshire or West Ridings I would think, someone there local to the area would know more. There is some info here about Westmorland
http://www.genuki.org.uk/big/eng/WES/
Says that parish records for Westmorland churches are held at Kendal which is in the Lake District as well as Bishops trnscripts but does say they should be available through LDS and parish registers are also available on Hugh Wallis site, which you are probably aware of, but there are a lot of towns in Westmorland but there is other useful information on this site I did find Buckles in Brough under Stainmore, there was Robert Bucle who had a father Christopher Bucle in 1584, but that's after Buckles moved south, whether there is link a generation or two back, maybe? but the Buckles were aleady using the spelling Buckle that's in the Visitation not Bucle but you never know they may have retained the old spelling up North a bit longer, Sir Cuthbert had a brother James and Christopher born after 1533, a Christopher Bucles had a James in 1577 and Robert in 1584,so that may be the link and if so Sir Cuttbert isn't his ancestor but they share an ancestor there was a Robert Bucle born to Robert Bucle in 1563 , then there was Robert Buckle born to Robert Buckle in 1640 , Cliburn also has Robert Buckle I also checked parishes wthin a 5 mile radius of Brough the only other was a Robert 1845 Warcup I have checked several other but not all yet there are so many and no luck so far with the family names. But Sir Cuthbert isn't mentioned under Brough on the parish records but like mpost place there would be a lt missing. I don't have a Christopher 1699 sorry I thought we had sorted this before think it must be a typo for 1629, I do have couple after 1711 but you would have those too