Originally Posted by
Often1
The UK is not in Schengen. Not sure what your point is.
The point was that you mentioned "EU control" and "Schengen" in your earlier post when what was meant by the OP saying "EU" was the UK/EU immigration desks at the UK border in LHR. Nobody is entering or leaving Schengen.
Originally Posted by
Often1
There is nothing wrong with asking at EU control for a stamp in your US passport as well. Just explain that you are a collector. The stamps do not serve any significant purpose any longer, other than entering and leaving Schengen and thus officers are much more understanding.
The OP wants a UK entry stamp in their US passport, but as an Irish citizen they are free from UK immigration time restrictions.
The UK entry stamp generally used for US passports states "LEAVE TO ENTER FOR SIX MONTHS. EMPLOYMENT AND RECOURSE TO PUBLIC FUNDS PROHIBITED". If the OP enters on an Irish passport they are not subject to these restrictions and it would be illogical to then restrict them in this way on another passport.
Therefore I believe they would need to enter the UK on the US passport only; but to avoid lengthy non-EU queues, they could just join the UK/EU queue since UK immigration officers will process anybody who presents themselves.
To avoid being accosted by civilian employees of Heathrow, they should have the Irish passport out when entering the UK/EU queue, making up an excuse such as "it doesn't work" if redirected to the e-gates.
The above is based on my observation of an exchange between an American+EU citizen at LHR: the immigration officer said something along the lines of that they could stamp the US passport but this would mean they couldn't enter the UK as of right as an EU citizen simultaneously; there was no problem with this because they were just on a day transit to mainland Europe anyway.