Hello Hawk64, a little late but here goes. I believe I am a direct descendent of Henry Thomas Cole via his daughter Mary Ann born 1828, then via Samuel Driver Meredith (Limehouse), John Silas Cole Meredith (Limehouse), Mabel Rose Meredith (Holborn, probably Stoke Newington) then my dad (Otago, New Zealand).
You've opened a can of worms for me because Henry Thomas seems to appear out of thin air around the time of his marriage, if his name was William then that answers a few things.
For me, things get doubly complicated because my mum was from Limehouse too, her grandmother was a Cole and her 3rd great grandfather was called Henry. Both Henry Coles have Bethnal Green addresses at various times so you start wondering if you are related to yourself in the way of the Royal Family :-) I'm now certain they a different people and I cannot make a family connection so we can put me being a bit inbred to one side.
I can only tell you what happened to the descendants of Mary Ann Cole as far as John Silas Cole Meredith lived 1869 - 1940 died in Stoke Newington London, his daughter Mabel Rose married a Kiwi in 1916, I think he was a seaman, his name was Francis J L Jones and they had a son called Donald James Jones. Mabel and Donald sailed for NZ in 1919 on the HMT Kigoma. Something happened on the way according to my dad, she got on to the ship as Mrs. Jones and got off Mrs. Thomson the wife of my granddad the Bosun. She had three more kids by my granddad in Otago. She committed suicide in 1943 aged 47. I also knew Albert Meredith (1908) the son of John Silas Cole Meredith as a kid. He lived in Princess May Rd, Stoke Newington.
Francis Jones died in Christchurch in 1966 and Donald died in Palmerston North in the 90s. Hope that this is of interest to you.