I think the "bath" is the long "a" vs short "a" split[0] (usually associated with north of England vs south of England) rather than r insertion. There is however something called the "intrusive r" among "non rhotic" speakers "such as those in most of England and Wales" [1] which I learned about thanks to this recent research, where "r"s are inserted where they don't exist, e.g. "supernova-r-in the sky" and "law-r-and order".

[0] https://en.wikipedia.org/wiki/Trap-bath_split

[1] https://en.wikipedia.org/wiki/Linking_and_intrusive_R

>"such as those in most of England and Wales"

Aren't Welsh dialects generally rhotic?

They are not adding an r. That's a long a. True, they are pronouncing bath like many English people would pronounce barth; but that is without an audible r.

It's not rolled, but if you don't call that an "r" sound then there's no "r" in many areas of UK. It's different to a long a, it's like a shortened "r" with no roll and the tongue further forward, but not as hollow as a long a.

Presumably you think "hearth" doesn't have discernible "[a]r" sound either?

> if you don't call that an "r" sound then there's no "r" in many areas of UK.

By itself, that is not a compelling argument. There is in fact no postvocalic R in many areas of the UK.

I think what I'm referring to is that shown in the map (1950s) at https://en.wikipedia.org/wiki/Rhoticity_in_English#Distribut.... The alveolar and retroflex variants, which to my ear give an r sound distinct from, for example [ɑː].