This question arises all the time because they have never published a clear policy. They will, however, tell you their policy in a letter if you write to them.
You should join the EU queue if you are married. Their policy is not to separate families during immigration control, and they will take all reasonable steps to avoid separating families. But since your question involves a girl friend, this policy does not apply. So if your girlfriend joins the EU queue, she would expect a sharp rebuke and instructed to join the non-EU queue. This is especially true if there are lots of people arriving and they are busy.
Note: There have been occasions where an EU/non-EU couple used the non-EU queue and were simply waved through by the IO. This makes the non-EU person an illegal entrant. Don't let it happen.
In the past, under the last government, some of these checks were
lifted at times of pressure on the border.
In the summer of 2008 Warnings Index checks were suspended on EEA
nationals - children and adults - on Eurostar services. At Calais,
Warnings Index checks were suspended on European Economic Area and UK
car passengers - again, adults as well as children were not run
against the Index. Since 2008, at various ports and airports, this
happened on more than 100 occasions.
Officials have told me that once, in 2004, local managers at Heathrow
Terminal Three decided to open controls and no checks were made.
Source: Ministerial Statement 7 Nov 2011
See also HC1647 Report (costs GBP 14.50)
See also Oral Evidence given to the Home Affairs Committee 26 March 2013
See also What happens when someone inadvertently enters the UK without a landing interview?
So you and your girlfriend should both join the non-EU queue if you want to transit controls together. Of course you can separate, but this strategy leaves your girlfriend vulnerable to a challenge about your whereabouts. Finally, if all the queues are empty and the IO has his 'leave to enter' stamp and he's in a good mood, she MIGHT get an interview and stamp via the EU queue, but it's not a reliable strategy, especially following the scandals.
UK immigration queues are segregated by type of passport, not the visa that the person carries. EU/UK nationals can use either queue, but non-EU nationals who are not travelling as documented family members need to use the queues as explained above.
Source: Border Force site