I do not know where in the UK William Mountcastle came from. It's interesting that Burke's info stated he settled in SC and married Susannah Moore. He married her in 1804 but in Prince George Co., VA. Their marriage is noted in the Petersburg, VA. newspaper. They later went to Edgefield Co., SC, then to Rogersville, Hawkins Co., TN.
By the way, Susannah Moore was a first cousin to Ann Hill Carter Lee, General Robert E. Lee's mother.