LONDON — Struggling to secure support for a minority government, Prime Minister Theresa May of Britain put forward a scaled-down legislative program on Wednesday that would prioritize the country’s withdrawal from the European Union and would jettison policies likely to struggle to pass in Parliament.

Mrs. May, who has been trying to secure a deal with 10 lawmakers from the Democratic Unionist Party in Northern Ireland, needs their support after her Conservative Party lost its parliamentary majority in a general election two weeks ago.

The government’s legislative agenda was laid out on Wednesday in the Queen’s Speech to Parliament. It had been scheduled for Monday but was postponed because of the political uncertainty.

The queen’s role in presenting the agenda is a significant ceremonial duty. Buckingham Palace announced Wednesday morning that the queen’s husband, Prince Philip, had been hospitalized Tuesday night “as a precautionary measure, for treatment of an infection arising from a pre-existing condition.” Prince Charles, the heir to the throne, accompanied the queen to Parliament, in place of Prince Philip.

Mrs. May is fighting for her political life. Not only has she been blamed by many in the Conservative Party for a disastrous election campaign but she was also widely judged to have mishandled the aftermath of a devastating and deadly fire at a London high rise last week.

Talks with the 10 lawmakers from the D.U.P. have proved much harder than expected. But even though Mrs. May’s position remains fragile, most analysts say that she is likely to secure their support one way or another.

The D.U.P., which has strong Protestant roots, has a major incentive to find common ground with the prime minister: Without its help, Mrs. May’s government could fall, and power could pass to the opposition Labour Party of Jeremy Corbyn, who has a history of close ties to Irish Republicans.

The crucial test will come next week, when lawmakers are to vote on the program in the Queen’s Speech.

Even if Mrs. May were to prevail, as expected, she would still struggle to pass contentious legislation. That being the case, the legislative program on Wednesday suggested that she had dropped several measures that were once centerpieces of her political agenda.

That explains why there was no reference in the speech to proposals for more grammar schools, which use tests to determine admissions, and why it made no mention of plans to require older people to pay more of the costs for long-term care at home — a proposal described by critics as a “dementia tax.”

The Queen’s Speech also made no reference to a state visit to Britain for President Trump, suggesting that it would not take place soon.

In many respects, the address highlighted the extraordinary speed with which Mrs. May’s fortunes have declined. At the start of the election campaign, she was well ahead in opinion polls and was expected to secure a victory large enough to reshape British politics. But much of that support has evaporated in recent weeks.

The speech reflected Mrs. May’s desire to make Britain’s withdrawal from the European Union, known as Brexit, her top priority, with several bills intended to provide the legislative framework for the move.

That approach presents its own perils, however, because the general election failed to deliver an endorsement of the clean break with the bloc that she wanted — one that prioritizes control of immigration over economic interests.

Although the Labour Party accepted the outcome of the referendum on withdrawing from the European Union, it wants to keep closer economic ties to the bloc and it could try to obstruct crucial parts of the government’s Brexit-related plans.

Yet if Mrs. May softens her stance on withdrawing from the bloc to accommodate pro-Europeans worried about the British economy — including some members of her own cabinet — she risks a rebellion from leading supporters of the withdrawal.

That would include possible successors like Boris Johnson, the foreign secretary, and David Davis, the cabinet minister responsible for negotiating Britain’s exit from the European Union.