Mary Ann COLES may have been the Mary Williams who was buried 14 Sep 1843, St Botolph without Bishopsgate, whose funeral was somewhat costly by comparison.

She married Joseph WILLIAMS 2 May 1776 at St. James' Clerkenwell, London.

1. Joseph WILLIAMS, baptised 18 May 1777, and buried 31 Dec 1778 - St. Boltolp Without Aldersgate.
2. Mary Ann WILLIAMS, baptised 16 Aug 1778, and buried 16 Aug 1778 - St. Boltolp Without Aldersgate.
3. Mary WILLIAMS, baptised 9 Jan 1780, and buried 9 May 1780 - St. Boltolp Without Aldersgate.
4. Ann WILLIAMS, baptised 9 Jan 1780, and buried 27 Mar 1780 - St. Boltolp Without Aldersgate.
5. George Henry WILLIAMS, baptised 2 Sep 1781 - St. Boltolp Without Aldersgate.
6. Isaac WILLIAMS, baptised 29 Sep 1782, and buried 6 May 1785 - St. Boltolp Without Aldersgate.
7. James WILLIAMS, baptised 3 Oct 1784. May have been the “[blank] Williams child ” buried 3 Aug 1785 - St. Boltolp Without Aldersgate.
8. Joseph Orchard WILLIAMS, buried 21 Dec 1787 - St. Boltolp Without Aldersgate.
9. Joseph Orchard WILLIAMS, baptised 4 Jan 1789, and buried 17 Mar 1795 - St. Boltolp Without Aldersgate.
10. James Biggs WILLIAMS, baptised 9 Jan 1794 - St. Boltolp Without Aldersgate.
11. Jane Bigg WILLIAMS, buried 12 Mar 1795 - St. Boltolp Without Aldersgate.

In the hunt for Mary Ann's birth, I happen to notice that a Mary Coles was baptised 5 May 1747, and recorded in the register of St Mary Le Bow, London immediately before Ann Williams - Ann being the sister of Joseph Williams:

Sadly, this baby was buried on the 6 Oct 1747, but led me into seeing if the couple, William and Mary Coles, had other children:

1. William Coles Baptism 11 Mar 1734 - Burial 10 Jun 1736 St Mary Le Bow, London
2. Mary Anne Coles Baptism 24 Jun 1736 - Burial 3 Mar 1737 St Mary Le Bow, London
3. Thomas Coles Baptism 20 Sep 1737 - Burial 24 Sep 1737 St Mary Le Bow, London
4. Charles Coles Baptism 7 Nov 1738 - Burial 8 Apr 1739 St Mary Le Bow, London
5. Elizabeth Coles Baptism 8 Jan 1739 St Mary Le Bow, London
6. William Coles Baptism 15 Oct 1742 St Mary Le Bow, London
7. Mary Coles Baptism 18 Aug 1743 - Burial 7 Feb 1744 St Mary Le Bow, London
8. Martha Coles Baptism 11 Mar 1744 - Burial 3 May 1799, aged 54 St Mary Le Bow, London
9. Mary Coles Baptism 5 May 1747 - Burial 6 Oct 1747 St Mary Le Bow, London
10. [Thos Coles Burial 8 Nov 1747 St Mary Le Bow, London]
11. Sarah Coles Baptism 16 Feb 1748 - Burial 7 Jul 1749 St Mary Le Bow, London
12. Mary Coles Burial 11 Apr 1782, aged 79 [1703] St Mary Le Bow, London

Clearly not the family I'm seeking, but enough to have me looking a bit deeper around the area…