ETA England

Yes, you have to enter the country to switch airports. Anytime you enter the UK you will need to have a valid ETA.

Thanks for quick response. It affects my son. I’m arriving and departing Heathrow, only changing from an EU flight to one to USA. Will I need an ETA, also?

Will you cross the UK border? If yes then you need an ETA.

If you are just connecting flights and don't have to go through immigration, then you won't need an ETA.

I’m not sure if I’ll go through immigration or not. first flight is Athens to Heathrow. Then connection is from Heathrow to Phoenix. I know when I did similar transfer from an EU flight from Copenhagen to a USA in Paris several years ago, I had to go through immigration in Paris. I guess I need to ask the airlines?

You encountered immigration in Paris as you entered the Schengen Area—there would be no further border crossing when entering Denmark.

You will need an ETA if you need to cross the UK border to get to your second flight. But if your journey is all on one ticket chances are you will not cross the UK border and will not need an ETA.

Ask your airline to be sure.

https://www.heathrow.com/connecting-flights

It is less than $15 and 20 minutes time to get your ETA.
Better to be safe than sorry.