I'm sorry, what I said was really confusing.
Right I will try and explain it better...
I am descended from James Tudgay of Longbridge Deverill. He had a bunch of children including William (c.1692) and John (c.1694).
Brian's website says that the William is possibly the ancestor of your William. John is the father of John Tudgay who (with Priscilla/Elizabeth - she used two names) had Thomas who fathered Priscilla who married John Morgan.
Your father is blood related to both of the people in the photos if he is from the Tudgay line as both of them are descended from Priscilla Tudgay. So your father and them would share the ancestor James Tudgay if Brian's supposition is right. I'm pretty certain all Tudgays are related anyway actually.
I had seen the Marshall and had wondered the same thing. I might look into the Romany Marshalls to see if there is any connection with the area.
I know very little of the Tugbys but I am going to look into those as well. I have a bunch of old Romany Routes that I am sure have information on them. I will look into the Marshalls and Tugbys this morning and get back to you on them.
Regarding the Romany name thing as well, I had also heard the theory that the name Tudgay came from the Romany word for milk & whey (can't remember exactly).
The Morgans ended up living in the Notting Hill slums. They moved all the way to London but went back to baptise some of their children in various places in Wiltshire. They were mainly masons which isn't a particularly Romany job but I have seen Romany masons several times before. They were also bird and dog dealers...a bit of a weird job, hawkers, labourers and then worked in the laundry.
The man who you said looked like you father married a Romany girl (she was actually a quarter Spanish/Portuguese Jew as well but mainly Romany). Her father was a marine store dealer, bricklayer's labourer, watercress seller, hawker/general dealer.
They used to have an old Romany vardo wheel in the back garden but it has sadly disappeared.
I have posted this link in another thread but this is the area that Priscilla's descendants (the Morgans) lived.
http://worley.org.uk/NOTTING%20DALE.htm