Given the date of that Times article, if he didn't marry until 1789 it must be his mother. It's interesting that there's little else on her family - presumably there's nothing mentioned in his will of them?
Interestingly enough, The Times article on his funeral describes him as 'not the most popular man in the world', and pokes a little fun at the expense of the funeral. Apparently in addition to the crowd that gathered at the church, there was a second crowd of pickpockets to take advantage of them. It seems they were at the Spring Gardens address even at that time, as it mentions the funeral procession going from Spring Gardens to St. Martin's.
Followed by this:
The Times, Saturday, Oct 18, 1788; pg. 2; Issue 1148; col A
Had the heir of the late Sir Robert Taylor given away the money among the poor of the parish, instead of entertaining the vestrymen with a supper, it would have been more honorable, besides giving comfort to those who are in want of the common necessities of life.
The Times, Monday, Jul 21, 1834; pg. 3; Issue 15535; col E
- describes Michael Angelo as the 'uncle of the Marchioness of Londonderry', apparently having at some point refused to give his permission (while she was still a minor) to her marriage to the Marquis of Londonderry, resulting in Chancery proceedings.
The Times, Wednesday, Jan 23, 1833; pg. 4; Issue 15069; col C
- is the death of the Marichoness Dowager of Londonderry, relict of Robert, first Marquis, and mother of Charles William, Marquis of Londonderry. Charles William must be the one who married Michael's niece, whoever she was.
http://www.wynyardwoodlandpark.org.uk/WynyardHall.htm - shows that Charles William Stewart, son of Robert Stewart, first Marquis of Londonderry, married in 1819 Frances, daughter of Sir Henry Vane-Tempest. Frances was born around 1800. So I guess that's a dead-end - she was his wife's niece.