I entered EU (Manchester) proceeding from Amsterdam
When you landed at Amsterdam you entered the European Union, travelling between EU countries there is generally no customs check.
If the Dutch customs were not interested in you, it is unlikely that the Brits would be either.*
When you landed at Manchester, the UK Border Agency would have already known that you were on the flight and where you had come from, if customs had been interested in you the would have called you to one side and asked a few questions.
*It occurs to me that you did not really enter the EU at Amsterdam, you probably did not have your passport checked by the Dutch Border people.
But, your passport would have had a good looking at as you passed the UK Border at Manchester, whether you had flown directly from Argentina or simply arrived from another EU country.
As a side issue, be aware that while the UK is in the EU (for now), it is not a "Schengen Country".
When I travel form the UK to mainland Europe, I have to show my passport to get into Europe, and similarly on the way back I have to show my passport to get back into the UK.
However once in Europe, I do not need to show my passport to travel between countries which are signatories to the Schengen Agreement.
Eg Germany and France
No customs, no passport control, just a sign telling which country you are about to enter.
This picture was taken at a barrage across the Rhine river near Marckolsheim in the Alsace region.
Happy holidays (and thread drift).
JimB