Transactions of the Cumberland & Westmorland Antiquarian & Archaeological Society is a long-standing local history periodical.Volume 4 (new series), 1904 is available online here. An extract of interest is reproduced below:

pp316-317

"Sir Edward [Radcliffe], bart., 1622-d. 1663
On his accession Sir Edward, with his brothers Francis and Cuthbert, enfranchised for the sum of £1441 his sixty Keswick tenants, among whom were Joseph Hechstetter, the head of the German miners, and Joseph Hechstetter's father-in-law, John Banks, father of the lawyer Sir John Banks. But his chief attention was devoted to the enlargement and rebuilding of his mansion at Dilston, which had already been begun in the time of his father.
He was rich and prosperous. In addition to his patrimony he had acquired large estates in Yorkshire by his marriage with Elizabeth, daughter and heiress of Thomas Barton of Whenby*. In 1629 he had bought the manor of Alston from Baron Hilton ; and in 1632 the barony of Langley from the Earl of Annandale (Tract ii).

*Thomas Barton’s wife was Alice, daughter of Thomas Brathwaite, of Burneside, and sister of Richard Brathwaite (“Barnabee’s Journall”)"

Could this Thomas Barton of Whenby be related to John Barton of Whenby, who in 1528 is left property by Robert Barton of Mekil Ormeshead [Ormside]? (*Nicolson et al 1777 p515-517). Presumably this is the marriage between Barton and Brathwaite that explains the Barton arms that appear in Burneside Hall (*Transactions CWAAS v6 1882).