Hi again Joyce
My grandfather was born in Old Brompton and a lot of what is now known as Gillingham was New Brompton. I was born in Chatham and left there as a 3 year old but used to return to visit my grandparents who lived in Gillingham. Wikipedia gives this info: Today Brompton is a small residential area between Chatham Dockyard and Gillingham. Here is the link:
http://en.wikipedia.org/wiki/Brompton,_MedwayI haven't found Elizabeth TAW's death. She could have died anywhere between Kent and Hampshire. I haven't trawled through Gillingham looking for TAWs yet but must do at some point.
The IGI has no further children for Robert and Mary TAW who was Mrs COX and we don't have a baptism for your Jeremiah who married Naomi CAMERON. I think he was probably the youngest child born to Robert and first wife Elizabeth.
I'll keep having a search about.
Good luck with your hunting. It's good that Ron is finding some more lines in Hampshire.
Best wishes
Carol