Leaving the EU implies automatic exclusion from the EEA?

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This question is slowly percolating through the wall of noise around the UK's exit from the EU. More attentive folks are wondering if to leave the European Economic Area (EEA) a formal notification is required. I.e., if beyond triggering Article 50 of the Lisbon Treaty, in order to fully exit its social and economics commitments the UK needs to trigger Article 127 of the EEA Agreement.

This question is highly relevant for a simple reason: membership of the EEA was not voted in referendum, therefore the UK institutions - Government, Parliament and House of Lords - are not morally obliged to any particular course of action in this regard. If leaving the EU does not automatically exclude the UK from the EEA, it will then remain a full member of the so called "Common Market" with all the rights and obligations it entails.