Your post was only ironic because it was asking for correction and was a little incorrect itself.

"By" is better and more general so you could say "I went to London by/through Birmingham.", but "through" and "via" are usually better in the context of locations. Except, "by" has a slightly different meaning in this sentence "I went by (past) your house yesterday".
You wouldn't really say "through correcting" but it's quite understandable yet a little stilted.