Well, Irish arrivals (as in SNN, ORK and DUB) at LHR (and EDI and probably most other UK airports) still require the passengers to pass through customs but not immigration, so any flights from the ROI to UK (again, I can only verify this for EDI and LHR) need to collect their bags from a different baggage belt and then proceed through a customs check point before leaving the airport. At EDI this means passengers arriving from the ROI come through a door which bring them out after passport control, but directly in to the international arrivals baggage hall.
At EDI, arrivals from BHD and BFS were taken through a separate door from other UK arrivals. This was due there being a police check point as there is still a certain level of extra security for NI flights. Bags from NI flights arrive on the same belts as domestic bags, it is literally just an extra little corridor the arriving pax have to walk through.
At LHR I've never flown to or from NI, so I can't verify if the same set up exists, although all flights to the Island of Ireland depart from a different area to GB flights, so I am guessing that a similar set up exists.
For departing passengers to GB, NI and ROI, there is the extra check point in place at T1 (it's done at the gate in T5) which shows that those passengers have met the required immigration standards to proceed to the gates. If you arrive from an international flight and are connecting to a GB/NI/ROI flight you get your picture taken to show you've gone through immigration. When you check in for a domestic flight, you get your picture taken at the main security check point, or at the check in desk (depending if you go to a desk which does this). When you get to the second check point (which you must go through to get to the GB/NI/ROI gates) they simply match the picture associated with your boarding pass and if all is well they let you proceed.