I was wondering when someone would mention what is in the previous post.
Just looked it up on IMDb.

Actor David Haig, this interpretation is his baby.
He wrote a theatrical play, to start with,
which opened in 1997.

The filmed version (Masterpiece Theatre?) was ten years later.
Haig plays Rudyard Kipling, and as you say,
Daniel Radcliffe is John Kipling.

Charmion, thank you for your attention to Kipling's original,
the details are new to me although they don't surprise me.
It also doesn't surprise me that people, like actor/writer David Haig,
would re-interpret the story to make it more appealing.
I saw the film when televised in the United States.
It focuses entirely on the father-son tragedy,
and makes much of John Kipling's American-born mother.
Then at the end, there is a heart-to-heart
between Rudyard Kipling and his monarch, George V, who has just endured
the loss of his epileptic son John ("The Lost Prince").
To his grieving king, David Haig, as Kipling,
recites 'My boy Jack' and that is how the film ends ...
very moving ...
and no mention whatever
of John Travers Cornwell.