Is there still a reason to do the IR(R) if you can do the EIR? The IR(R) will give you approaches in OCAS, limited to UK but EIR will give you CAS (airways, etc) but no approaches all over Europe; it seems to me the EIR is a better stepping stone towards a full IR.
I am sending my daughter off to do the EIR as soon as she finishes the PPL.