"NEST OF DOVES"
If Britain places limits on the free movement people, one of the EU's core principles, it will lose its access to the single market, governments on the continent have warned.
Banks in the City of London are worried that they could lose their right to sell services across Europe if May insists on curbing migration under a deal with the EU-27.
After bracing for a potentially difficult summit, the aide to May said the atmosphere had been "constructive" and said the prime minister had sought to prove that Britain was still an active member of the union by supporting action against Russia over Syria.
EU diplomats said May had intervened at numerous points during the evening, not only on Syria but also Europe's migration crisis, a topic she dealt with as interior minister.
During a discussion of plans the other leaders made without her at a summit of the EU-27 last month, she spoke up to say that Britain should not be excluded from decisions while it remained a member.
It was not quite the "nest of doves" that Tusk had promised earlier when asked whether May was entering the lions' den.
Leaders were clear that they would not allow Britain to "cherry pick" the profitable parts of their union, such as free access to the market for certain sectors, without taking on the full responsibilities of membership.
At the tail end of a dinner of scallops and lamb, May set out her approach to Brexit, underlining there would be no second referendum and that she wanted Britain's departure from the EU to be "smooth and orderly" to safeguard the economy and calm increasingly nervous investors and markets.
There was no discussion after she spoke, an EU diplomat said. "May stuck to her speaking notes," the diplomat said, echoing frustration in some European capitals that they have gained little from the British prime minister beyond her oft-repeated mantra that "Brexit means Brexit".
Hollande told reporters that May had pledged to enter discussions in a constructive spirit, before adding: "We'll see."