Hi Greg,
Further to Gail's comments, William Gilbert (1805-1890) whose wife was called Martha, was a silversmith, watchmaker and jeweller at High St and Donegall Sq, Belfast. I know about all his descendants, including one of his daughters Sarah Gilbert, who was my great great grandmother (and sister of Emma Gilbert mentioned by Gail).
I know that William's mother was called Sarah, born 1781. I'm pretty certain William had brothers James, born 1808 and Edward, born c1814. I don't know anything about these 2, except that both died in their 30s.
As far as I know, all these Gilberts remained in Belfast and I'm not aware of Ann Penelope Gilbert or a connection to London, so like Gail, I'm interested to know what connection you have made.
Helen