Greece has announced today, that it is has sent letters to the British government, in order to initiate a mediation process via UNESCO. I have known about this proposed initiative for some time, but was unable to say anything about it before the news became public.
If the mediation proceeds, it will be a test case for UNESCO (or more specifically the Intergovernmental Committee for Promoting the Return of Cultural Property to Its Countries of Origin or Its Restitution in Case of Illicit Appropriation). The rules for mediation were brought in a few years ago, but this will be the first case to use them.
I think that it is a great step forward, as for a long time, the lack of proper political action from Greece has left the British Museum in a situation where they feel that they are sitting comfortably with nothing that they need to respond to.
You can read the full rules under which the mediation will take place (if the UK agrees to enter into the process) here .
Greek Reporter 
UNESCO Mediates Parthenon Marbles Fight
By Maria Korologou on October 3, 2013
On October 6 in Athens the International Conference of committees will be held, which is a very important moment for the effort to return the Parthenon Marbles.
After the meeting of the Greek Minister of Culture and Sports with the Director-General of UNESCO in July 2013 in Paris, during which Panos Panagiotopoulos asked from Irina Bokova to exercise her personal and institutional influence in order for the mediation process with the British side to be initiated, the leading international organization for culture addressed a letter to the British Foreign Secretary William Hague, the Secretary of State for Culture, Media and Sport Maria Miller and the Director of the British Museum Robert Neil MacGregor.
With this letter the British officials are officially informed of Greece’s demand to go on with the mediation process in order to achieve a settlement of the dispute on the repatriation of the Parthenon Marbles.
If the British side agrees to carry out this process, it will be the first time that UNESCO will have taken action to solve a cultural dispute between two states.