Which queue for an unmarried EU/non-EU couple travelling through UK Immigration Control together?

Stay together and join the Non-EU queue.

However, as mentioned above, sometimes special circumstances apply. For example, my partner and I are British/Australian and my partner has a British residency card. We usually just grab an immigration customer service officer (one of the ones walking round and checking everything is proceeding correctly) and show our passports and the residency card and ask if we can join the EU queue. Usually they say yes.

Make sure that your girlfriend (as a Non-EU person) completes an arrivals card, and that the Non-EU passport is appropriately stamped (or else you will have exit EU issues!).

You may be able to get your girlfriend an EEA family permit as your "unmarried partner," if you can show that you and she are "in a lasting relationship." See https://www.gov.uk/family-permit/eligibility for more information.

Because you are a UK citizen, you must also show that you are "exercising your treaty rights" by living (or by having lived) in another EU/EEA country. If you cannot show that, then you must enter under UK law rather than EU law. See https://www.gov.uk/family-permit/surinder-singh for more information.

The EEA family permit is free of charge. If you get one, you and your girlfriend will both be traveling under the EU right of free movement, and you would therefore both be eligible to use the EU line at the border.

In theory, if your girlfriend qualifies as your unmarried partner, and she is from a country whose citizens normally do not need visas to enter the UK, you don't actually need the EEA family permit. But then, to use the EU line together, you ought to have evidence of your unmarried partnership to show the border officer if you are challenged. Getting the permit beforehand would remove this requirement, and, since it is free, the investment is only one of time.

Also, in the past, before I knew any of this, I took my then-girlfriend, who was traveling on a then-non-EU passport, to the EU line in a London airport. I said to the officer, I wasn't sure if we should both come to this line together, and he said, well, no, you're not supposed to, and then he processed us without further ado. That was perhaps 8 or 10 years ago.