So there's a few types of upgrades:

UuA: upgrade using avios
AUP: airport upgrade
POUG: pro-active online upgrade
Fare difference: what is says on the tin

The 3,000€ that you're quoted fro MAD to LHR sounds like a fare difference quote - presumably you've either done self service online or phoned them to get that price.

As you're booking connecting flights, it is highly unlikely you'll see POUG offers (which appear in manage my booking). However for MAD-LHR this would usually be around €175 - €250.

You can ask at the airport about an AUP. These can be bought at check-in desks or BA lounges. For MAD-LHR they may be between €125 and €250, sometimes more, very occasionally less. You obviously have to wait until the day of the flight to find out whether you can buy these.

To upgrade using avios you have to book with a BA ticket number (125 ticket stock). If you're booking on the AA or Iberia website then you'll not be able to upgrade using avios. You can upgrade AA and IB flights with avios but you have to be on a BA ticket. Obviously there has to be avios availability, which depending on your route could be hard to come by. You might have better luck on LHR-JFK say than LHR-PHL.

If you post an example itinerary that you'e booked we can help a bit more.

EDIT: There's obviously on more type of upgrade and that is the coveted "op-up". To be honest, you've already done the most you can do by booking into Premium Economy which usually has the most op-ups, however if you're lucky, one day BA may have to upgrade you for operational reasons.