I listened on tv that technically the title now belongs to Charles, as the eldest son. What was announced at the time of Edward's wedding was:
“The Queen, The Duke of Edinburgh and The Prince of Wales have also agreed that The Prince Edward should be given the Dukedom of Edinburgh in due course, when the present title now held by Prince Philip eventually reverts to the Crown.”
The title will only revert to the Crown when Charles ascends to the throne, like all other of his titles. If he dies before becoming King, William will have title. So at this point, Edward will only get the title when QEII dies/abdicates.
Someone like lovecharles could confirm this?