An EU official confirmed that it is for the United Kingdom to make a notification of the activation of Article 50, and that this is a legal act. The referendum itself, the source confirmed, cannot be considered a trigger of Article 50 in itself. This means that the process of the UK leaving the EU does not start until that moment of notification no matter what all the EU stakeholders say.
Although EU leaders have asked the UK to trigger the process as soon as possible, the EU official would not comment further as to what happens if the UK does not activate that process.
Update: A European Council spokesperson has confirmed that Article 50 must be triggered formally by letter from UK to the European Council President Donald Tusk or official statement at European Council meeting.