Also see this very similar thread
At airports, you can get into any queue. The queues are mainly for the convenience of the Border Force staff, which is why different airports will have different protocols for who can enter into the British/EEA citizens queue in a scenario like yours.
The worse that can happen, and it can happen, is after getting to the front of the EEA citizens queue, you will be sent back to the non-EEA citizens queue and start the journey back there.
Understand the difference between the two queues. In the British/EEA citizens queue, the Border Force officials only need to carry out verification of identity and cross-checking the validity of the passports/identity cards. That is to say, the right of the people in that queue to enter the UK is generally straightforward to ascertain.
In the non-EEA citizens queue, the right of people to enter the UK is not so unqualified (even after ILR. You still only have a revocable Leave to Remain). There are further checks, including those conversations that they have with you at the desk.
Therefore, if you are at the wrong desk, the Border Force official may either send you back to the non-EEA citizens queue or may conduct the checks themselves. It will depend upon them, not upon you.
Given that you would waste more time if you went through the EEA citizens queue and then were sent back to the non-EEA queue, and given that you will soon apply for British citizenship anyway, I would counsel you to go to the Non-EEA citizens queue this last time.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.