Cousins, we see here that Eliza was sometimes called Elizabeth. The witness William Green may have been Eliza's son William Goodall Green. Or maybe not.
This is a form they filled out. I'll put the handwritten part in italics.
from the Parish Registry of Marlebon page 34, year 1809, FHL British film 584228
No. 101 Thomas Esdaile esq of Bognor in the County of Sussex Bachelor and Elizabeth Green of this Parish Widow
were Married in this Church by Licence this Eight Day of July in the Year One Thousand Eight Hundred and nine By me Benj'm Lawrence Curate This Marriage was solemnized between Us Thos Esdaile Elizabeth Esdaile