I am a "Doddimeade", in fact I believe Martin is a distant cousin of mine and I have been in touch with him.
I have previously worked for a company which had access to the electoral role and I found approximately 12 Doddimeade's, all of whom I could account for as relatives.
I know of a few variations, and all have turned out to have some connection to my family tree, so it is a fairly unique name.
I'm not comfortable giving out my personal details, nor the details of my own research, but I would suggest to you that the "Dodimead" you seek shares her roots with my family.
Our family name traces it's origins to the Celts and can be found as far back as Roman occupied Britain. I do know that it has strong connections to Cornwall and Devon, which ties in with the Celtic connection and your connections to Somerset.
A great many of my more recent relatives (last 100 - 150 years) had moved to the London area, myself included, although I no longer live there anymore!
I would suggest you look out for "Doddimeade", "Dodimeade", "Dodymede" & "Dodimede", all of which I have come across, as well as "Dodimead". I have even found a "Doddimead" imigrant who turned up in an old library archive photo in Australia, so be prepared for quite a lengthy search regarding our name!
Regards.