Just to add-
I have romany (travelling) families from Kent with the surname Matthews, and your Matthews family seem to be travellers from what i've seen. Even though in the late 1800's and so on they're not living in caravans or tents, they could still be from a travelling family.
In the 1939 register their jobs are farm work and fruit canning, which similar to hop picking was a popular job that travellers did in Kent to make money.
Another pointer to a travelling family is the name of James' brother ''Ambrose''. This is a very common traveller given name.
Have just gone back on the Garrett side of the family and have actually got back to some of them living in a Caravan in West Ashford. If you want to know how I got here then I'll explain further but you may already have this
! The jobs they have are Hawkers, a very common traveller job. The surname is actually Ripley but they married the Garrett family, so they come from that side. I'll have a look to see if I can find any Welsh links quickly. The same family on the previous census: (this had been written about them) ''Family had travelled during the night and arrived in District No7 in the morning of the 18th but had not been spoken to concerning this census.'' So 100 percent travellers!
In fact, I have some Ripley's on my family tree that would be on yours! (Moses Ripley 1847-) also have a picture of Moses' son George Ripley. I can go back on the Ripley side for you if you would like.
Just to summarise for the Ripley's:
Nora Matthews----> Maria Garrett(1899)----> Celia Ripley(1870)----> George Ripley(1831)----> George Thomas Ripley(1807) ----> Mark Ripley(1784) ----> Mark Ripley(1738)----> Thomas Ripley(1718)----> John Ripley (abt. 1700).
This is what I already had for the Ripley family on my own tree (plus adding in the Garretts at the start for you). So can confirm the Ripley's aren't the Welsh side, although the Garretts may be.
Please ask if you want anything explained or don't understand what i've written, I can help you find the census' for what i've found.
Good Luck