I carry multiple passports as well. When I arrive into the UK I use my British passport. Whenever I check in for a flight I present the passport for my destination point, for example: if I�m going to Australia I present my Australian passport, if going to Canada I present my Canadian passport. When I leave Australia I present my British passport at check-in, but I use my Australian passport when I go through passport control. (remember, the boarding pass doesn�t show your passport details)
Once back in the UK I simply clear through the UK/EU channels.
To help you understand better: the carriers have an obligation to ensure that you are legally documented for your arrival. Flights to destinations such as the US are �pre-cleared� using the data that has been scanned in by the airline. The most simple thing to remember is that when you arrive in your �host country� (the country of which you are a citizen), you are obliged to present only that passport and none other.
With the Americans, it wasn�t too many years ago that if you had presented a passport that was not American, knowing full well that you were an American citizen and were in possession of that passport, it was considered an unwritten act of treason. Thankfully, most �reasonable� countries now accept the duality of human lives and the probability that many may have two or more passports.
After all of this, however, I will say that with any country that requires an entry and exit visa, you must, in every instance, only use that one passport. Otherwise, you could find yourself in a bit of hot water.
I hope this helps.
Fr Bill