This ぬ is an old form of the negation, ない. See for example this post. The fact that the sentence uses ぬ leads me to suspect this might be some well known saying, but that's a pure guess.
想い通りにはいかぬ --> 想い通りにはいかない = "does not go/proceed according to expectations".
You say you already understand the grammar of ばかり, which is good because I find it difficult to explain. But I guess the literal, highly clunky, translation would be "this world is in a state where things (こと) do nothing but (ばかり) not proceed (いかぬ) according (通り) to expectations". Which, when you get your head round the double negative, means what you want it to mean.