Thank you for that Hugh.
It's all starting to fall into place now as I have just found a reference to this Alexander Whiteford by his granddaughter who says that he "was born at Cross House, Antrim where his ancestors had lived for many generations" and that it was "his hospitable mansion". He is described as a "noble hearted, loyal old country gentleman, who marched bravely in command of a company of militia, at the early age of 17 years, and rendered his country good service in the Rebellion of 1798".
So now I just need to pinpoint where exactly Cross House was, although I am assuming it was part of the Cross Hamlet in the Cross Townland that Capt Jock pointed me towards. It would also be good to find out more about Alexander's participation in the 1798 Rebellion and his membership of the militia.
From what I've found so far, it seems that Alexander or his father, who was also Alexander, leased about 700 acres in the Cross Townland (which must have been just about the whole of Cross Townland) from Col Hugh Boyd who had purchased the village of Ballycastle from the 5th Earl of Antrim in 1727.
Thank you very much again for taking the time to reply to my post.
Paul