Recent row with BD staff has left me with the following impression regarding baggage transfer at LHR: all baggage can be connected via LHR, it is just the physical transfer of bags through that is the difference. If you have a connecting flight on the same itinerary or confirmation booking, then your bags will be sent all the way through to your destination. If your connecting flight is not on the same trans-atlantic itinerary (BD or not BD regardless which can mean two separate BD tickets), then you have to lug your baggage to Terminal 1 and have the BD staff at check-in take your bags - remind them that you are connecting to get your 2 (or 3) 'North American' bag allowance rather than your 20kg normal BD allowance. Thus, all baggage is accepted but may be done in different ways.

With my experience of transferring to the "UK, Channel Islands and Ireland" part of Terminal 1, you'll still have to go through a 'mini' passport clearance (I say mini as you will have no bags with you) area just after getting off the transfer bus and up the escalators by the FCC area. This is MANDATORY and regardless for those transferring to the rest of the UK, Ireland and Channel Islands from any international flight from any other terminal other than Terminal 1. If you decide to exit Terminal 3 (maybe to use the ML Arrivals lounge), then you'll clear customs in Terminal 3; no customs after that obviously even if going to T!.

As in my usual situation, if going to Ireland, you'll then go through customs AGAIN (but Irish this time and with bags) in Dublin.

However, once you are in the UK, I didn't think you had to clear customs in EDI again?

After the Aug 1st interline baggage fiasco start, I have tried on several different flights to get my separate ticket BD BP to Ireland via LHR from Canada - to no avail and have had to bring luggage to and get my BD BP in T1 myself.