I heard this yesterday on an AM-radio gardening show.

Problem:
The two prepositions are overkill.

Explanation:
The prepositions “up” and “on” rarely go together, and this is an example of their NOT belonging together.

The person who spoke “When I was reading up on that, …” was a caller on an AM-radio show about gardening. He was telling the show host that he had been reading about a particular gardening topic.

This gives us the clue: the single preposition “about” should replace the two prepositions “up on” in the sentence.

I believe that the caller’s replacement of “about” with “up on” is consistent with my “Devolution toward Simpler” hypothesis. It’s simpler to say “up on” than to say “about” because the “n” in “on” can be said quickly whereas the “t” in “about” must be held longer for recognition by the listener.

Solution:
“When I was reading about that, …”