When the CPS decided against prosecuting Mr Ali itself, the CAA brought a private prosecution.
But, shortly before this was due to come to court in July this year, the CPS intervened and blocked it, arguing there was insufficient evidence for a conviction.
The CAA announced it would challenge this and on Monday it said it had won the right to contest the CPS decision at a judicial review.
In a statement, the CAA said the Honourable Ms Justice Lang had granted the application for a review as it raised “important issues”.
CAA chairman Gideon Falter said: “This is a case that the CPS should have prosecuted itself.
"Our emphatic legal advice is that their decision to prevent us from doing so was irrational, and we are encouraged that the court has agreed that our case should proceed to the second stage of this two-stage judicial review process.
"We hope to succeed and resume our private prosecution of Nazim Ali.”
