Tom Hollander as Dylan Thomas

In the middle of the 20th Century Welsh parents who wanted their children to "get on" scraped together the money for elocution lessons. This was to make sure their children did not sound "common".
Thomas, Burton and Hopkins were all taught to shed their south wales accents.
Also my mother (who went right to the top of the exam system in elocution) and her cousin who went on to become a professor of literature. And I would seriously doubt that if cousin (who is 90 this year) had come with a broad Swansea accent she would have risen so successfully in her career in English universities.
Even 20 years ago a friend (with a Swansea accent) was turned down for a job as head of maths in a London school. When he rang the head to ask why they had chosen not to appoint any of the interviewees, he was told that his accent would not go down well with the parents. So right up to the end of the 20th C we see that prejudice against the Welsh accent was alive and well in the south of England.
Welsh accents are much more acceptable these days - even being allowed to read the BBC news! The aspiring parents in Wales these days send their children to Welsh language schools.

Why do aspiring parents send their children to Welsh language schools, Jess? Being fluent in Welsh is only going to be an advantage in the Welsh job market.

Yup ana but there are lots of jobs in Cardiff that require fluent Welsh and in the north where I am you could not get a job in the public sector without it (unless you have a very special skill, like A and E consultant)
And why, anyway, would you want your kids going off to work in England?

Anniebach I'm not familiar with Watford but there was something called a 'classless' accent that predominated in the commuter belt areas around London.

My two sons, in their childhood, didn't acquire any specific regional accent because we moved several times, finishing up in the South Manchester/North Cheshire area. I could describe their accent as 'classless', or non-specific, though definitely English.

Thank you suebaily, explains why I have never been able to connect their accent with, for example, a county most unusual accent

Jess, I take your point - but I don't think many North Wales kids would want to go off to work in Cardiff, either...

The London prejudice against Welsh accents you mention, Jess, doesn't seem to have applied further north. I worked in four FE colleges in the Midlands, East Anglia and Manchester. Three of them had Welsh principals.