One of popular story seems to be curry udon started at a soba shop Sanchouan (三朝庵) at Waseda in Tokyo, unfortunately this shop closed on 2018. Widely accepted story is that around 1904 the owner Sanchouan started curry flavored udon soup dish.

When Meiji Era started on 1868 Japan opened its border to outside, suddenly European and the U.S. culture flooded into Japan and anything European and the U.S. became very trendy, Traditional soba shop like Sanchouan was loosing business to more trendy European/the U.S. type establishments. Story has it that the owner of Sanchouan made curry flavor soup for udon and became a hit among young college kids form near by Waseda University.

But I also heard somewhere that the owner of Sanchouan was not the person who came up with curry flavor soup for udon. Other were already doing similar kind of thing and the owner of Sanchouan has decided to make own, some say that the owner of Sanchouan is credited for making curry udon popular.

P.S.
The owner of Sanchouan is also credited for katsudon. Story has it that Sanchouan was located at a college town of Waseda so the owner of Sanchouan frequently tried to come up with dishes liked by young college kids.