LONDON — It remains unclear whether Prime Minister Theresa May’s plans or timetable for taking Britain out of the European Union will be altered by the Supreme Court’s ruling on Tuesday that she must secure Parliament’s approval before beginning the process. Most analysts, even those who opposed “Brexit,” as the departure from the bloc is known, doubt that it will.

And Mrs. May had already said in her speech on Brexit last week that Parliament would have a vote on whether to accept the final deal negotiated with the European Union.

But the ruling Tuesday — which included a decision to deny the Scottish, Welsh and Northern Irish legislatures a veto in the matter — has brought to the fore some ancient tensions in Britain’s democracy, which has somehow made it through the centuries with an unequal union of four nations, an unelected upper house of Parliament and without a written constitution. These tensions may ultimately have far greater impact than a ruling that was widely anticipated.

“There are some fairly serious questions about how the U.K.’s constitutional settlement operates, not least the lack of democracy at the heart of the houses of Parliament,” Stephen Gethins, the Scottish National Party’s spokesman on Europe in the British Parliament, said in an interview. “All this raises quite substantial questions about the future of the union.”