I'll take a guess that it was in the Eastern Division Championship.
I remember reading an article in the Free Press years ago about Leeds v Doncaster being on TV. I've tried to find details on the BBC Genome project which lists every programme broadcast, but without success. Was it on ITV ?

Yes it was the Eastern Division game played at Headingley Leeds September 22nd 1962 Leeds 21 Dons 10 Attendance 8700 live broadcast on BBC Grandstand.

Can you give details of the first ever rugby league game to be broadcast on live television from Tattersfield?

Clue.
Roger Millward was a player in the game

v Hull KR or Cas ?

Sorry Paul it wasn't either of those two teams.

Wild guess, an international fixture of some description? (Trial or warm up game pre World Cup).

Sorry it's none of those.

Another Clue.

Two Counties.

Yorkshire v Lancashire
(Roses fixture)

You have got one of the teams correct it wasn't a roses match.