LONDON—Prime Minister Theresa May heads to her first Brussels summit of European Union leaders on Thursday as she wrestles to balance demands at home on how to extract the U.K. from the bloc.

With only a thin majority in Parliament, the premier faces a vociferous group of euroskeptic lawmakers in her party that seeks certainty that she is pursuing a hard break with the EU and that Britain will regain control over its borders. But she also is trying not to alienate the vast number of businesses calling for minimal disturbance to Britain’s trade relations with EU partners.

Several senior diplomats said Wednesday that other leaders at the EU summit will be looking to Mrs. May to clarify her recent remarks at the Conservative Party conference, which have been widely interpreted in Europe as setting Britain on course for hard break from the bloc and a loosening of economic ties.

Mrs. May plans to lay out her broad approach for taking Britain out of the EU over dinner with the other leaders on Thursday, according to a Downing Street official, emphasizing her view that a good deal for the U.K. is also in the interest of the EU.

But at home the British prime minister has resisted giving a running commentary on her approach to the negotiations, which she said she intends to open before the end of March. Her approach of centralizing decision making and relying on a close-knit circle of advisers has alienated officials in some departments and exacerbated differences between members of her cabinet, officials say.