Yes, basically those things add up to the fATPL. You will also need a Night Rating which can be done either before or during the CPL. Same goes for a Multi-Engine Class Rating if you do a ME-CPL and ME-IR.
If modular, the IR can be done straight after issue of the PPL but most schools recommend the CPL first. I think the ATPL theory exams also need to be completed before commencing a CPL, or certainly before issue.
Download LASORS 2008 from the CAA's website and that tells you everything in detail about the modular and integrated routes.