The Telegraph 28th July looked at Michel Barnier's background and they note that he is likely to be "a tough negotiator and take a hard line on EU rules." It seems that he has insisted that Britain will have to accept freedom of movement - "without exception or nuance" if it wants to retain access to the single market and also there will be no negotiation before notification of their farewell letter."
As almost everyone now knows, the exit route is via the Treaty on European Union Article 50.
Article 50(2) - "A Member State which decides to withdraw shall notify the European Council of its intention. In the light of the guidelines provided by the European Council, the Union shall negotiate and conclude an agreement with that State, setting out the arrangements for its withdrawal, taking account of the framework for its future relationship with the Union. That agreement shall be negotiated in accordance with Article 218(3) of the Treaty on the Functioning of the European Union. It shall be concluded on behalf of the Union by the Council, acting by a qualified majority, after obtaining the consent of the European Parliament."
TFEU Art 218(3) - "The Commission, ........, shall submit recommendations to the Council, which shall adopt a decision authorising the opening of negotiations and, depending on the subject of the agreement envisaged, nominating the Union negotiator or the head of the Union's negotiating team." [My emphasis].
I read this as saying that it is for the European Council, and not the Commission, to authorise negotiations and to nominate the EU's lead negotiator.
The last European Council meeting was on 28th June - see the Conclusions. The next meeting is in Bratislava in September. The 28th June conclusions report that the UK Prime Minister informed the Council of the outcome of the referendum. Nothing is recorded in the conclusions about the opening of negotiations (which would not take place unless and until the UK gives notice under Art 50 TEU).
On 29th June, the European Council (minus UK) held an informal meeting and made various observations about the UK referendum - see Informal meeting at 27 - Brussels, 29 June 2016 - Statement.
In June, it was announced that Mr Didier Seeuws had been appointed to lead a Brexit taskforce of negotiators. Mr Seeuws will be working for the Secretary-General of the European Council (Mr Jeppe Tranholm-Mikkelsen). The appointment of Mr Seeuws is considered at Open Europe 27th July where it is noted that:
"Article 50 states that the exit agreement between the EU and a departing member state “shall be concluded on behalf of the Union by the [European] Council, acting by a qualified majority, after obtaining the consent of the European Parliament”, and the Council has already appointed the veteran Belgian diplomat Didier Seeuws to lead its own internal Brexit task-force. Given the high stakes and political sensitivities around Brexit member states will want to maintain close oversight of the process as opposed to leaving it to the Commission (some member states place a large share of the blame for Brexit at the door of the Commission in the first place). In the end, it is the member states that set the negotiating mandate for the EU, meaning Barnier (as well as Juncker and his UK-sceptic Chief of Staff Martin Selmayr) could find their hands tied somewhat."
See General Secretariat of the Council
A very good, and detailed, analysis of the Treaty provisions relating to leaving the EU is by Dr Philip Syrpis (of Bristol University). Please see his article What next? An analysis of the EU law questions surrounding Article 50 TEU: Part One and also Part 2.
Also, please watch Chatham House 18th July - where Professor Sionaidh Douglas-Scott considers Brexit.
Via Twitter ....
This is right but I think he is just the Commission rep. The Council will appoint the actual lead negotiator. https://t.co/9NXRgoU6ZP— Sir Paul Jenkins (@sirpauljenkins) July 28, 2016