Students on an integrated course do not hold any kind of licence (until the very end).
As an IRI you can only teach the IR and IRR (to licenced pilots). During an integrated course the students are combining PPL, CPL and IR into one, so you need to be able to teach all three.
Unfortunately after your IRI you need to do an FI course, hour build 30 hours PIC on a MEP, then do the MEPCRI course. If you don't have the PIC time you're looking at another £20k+