- Get house in order -
One problem May faces is that even her own government cannot agree on its strategy for Brexit, with some ministers pushing for a clean break with the EU and others seeking continued ties to protect the economy.
Despite her tough talk at the Conservative conference, there were media reports this week that Britain may consider paying for single market access for key industries, such as the City of London financial sector.
Her timetable also risks being upset by a legal challenge at the High Court over her refusal to allow parliament a vote before she triggers Article 50.
A decision is due by the end of the year.
Another domestic headache is Scotland, which voted to stay in the EU and whose nationalist government is threatening a second referendum on independence if it is forced to leave the bloc.
"I suspect they will take the line at the summit that May has got to get her internal house in order before they even start talking," noted Professor Catherine Barnard, of the University of Cambridge.