Breckney Bed anciently would be in Lanercost Parish, the parish church being about five miles from the farm. In 1853 a new church of St Mary Magdalene was erected, just over a mile away, near Gilsland, so the family may have switched to that church. Breckney Bed is in the Ecclesiastical Parish of Gilsland. It is in the Civil Parish of Waterhead.
Quite often civil and church parishes cover the same area but not in this case. You won't find BMD records for Waterhead. Hope this helps.