Burford in Shropshire is the one associated with the Cornwalls, and that only since the marriage of Geoffrey de Cornwall to Margaret Mortimer (it was in the Mortimer family earlier, having come to them from the de Says etc etc etc). http://barony-of-burford.info/
It got a bit complicated, because the Lancasters also had a claim on Burford, and John Cornwall (c. 1364 – 11 December 1443) became the third husband of Elizabeth of Lancaster. John, not being in the direct line to inherit the barony, was made baron of Fanhope and Milbroke; but as he left no son to succeed him, the title became extinct.