There was a TV series based on "Black Beauty" in 1972. But although it was set in the original England, it had less to do with the novel than did the Americanized mini-series.....
'The Adventures of Black Beauty' is a British children's television drama series produced by London Weekend Television and shown by ITV in the United Kingdom between 1972 and 1974. It was distributed internationally by London Weekend International.
The series was not an adaptation of the book by Anna Sewell, but a "continuation" featuring new characters created by Ted Willis, most prominently Dr James Gordon, played by William Lucas, and his children Vicky, played by Judi Bowker (who became Jenny, played by Stacy Dorning, in the second series) and Kevin, played by Roderick Shaw. Other writers included David Butler and Richard Carpenter, while directors included Charles Crichton and Peter Duffell.
The series, which was filmed mainly at Stockers Farm, Rickmansworth, Hertfordshire, was widely acclaimed for its high production values and quality of writing and acting, and at times had remarkable English gothic overtones for a children's series.
There is a Black Beauty in Toobworld who is based on the horse in the original novel, even though the setting was changed to America. This version can remain in Earth Prime-Time, however, because in the end, it's just a name given to a horse. The plotline was completely changed.
As for the "recastaways" of Vicky and Jenny, both were Dr. Gordon's daughters. But he could only afford to send one off to finishing school at a time, so when Jenny came home, Vicky left for her schooling.