You're now in a tough situation, but I still see no reason why you didn't apply for the CPL immediately, and just sort out the IR paperwork once you'd passed that rating. They are entirely different courses, so as long as you have copies of things like logbook pages to prove to an examiner that you meet any requirements to take the IR test, I really don't see that you need the paperwork in hand.
Because you save a bloody fortune if you apply for them all at once.
Its a well trodden route to apply for CPL/IR/MEP all at the same time.
If its the schools fault with dodgy paper work go and see the citizen advice. Then with the legal facts in hand start talking to people.