It depends on the time of day etc, but there are I think three lanes - (1) e-gates, (2) non-uk passports that can't go to e-gates, (3) lanes for UK passport holders that are with children or just need the passports stamped. Generally, lane (3) is fairly quick. That's the lane you need, but, again f...

I went to see a border force officer, to avoid any issues of being an overstayer tourist. I told the officer that we're all British just didn't have time to apply for a passport and showed him the citizenship certificates. On a couple of occasions they didn't even look at those. Passports were not ...

Did you just enter using the e-gates with your Non-UK passport (American in your case) - without the ILR BRP card (essentially as a "tourist") and then just apply for the UK passport as per usual?