LONDON — Over the last few years, as Britain has divided into warring tribes over its exit from the European Union, Queen Elizabeth II has retained a sphinxlike neutrality, imperturbably getting on with the business of conveying knighthoods and hosting garden parties.

But this week even the queen was drawn into Britain’s constitutional turmoil, after a prominent lawmaker suggested she employ a royal prerogative that has not been used for centuries: the right to tactically adjourn, or “prorogue,” a rebellious Parliament.

The 92-year-old queen then made a veiled reference to Brexit in a speech on Thursday, delivering a plea for “respecting different points of view” and “coming together to seek out the common ground.” In line with her constitutional obligation to remain neutral on political matters, she revealed nothing about her views on Prime Minister Theresa May’s withdrawal agreement or, say, the northern Irish backstop.

[What is Brexit? A simple guide to why it matters and what happens next.]

“As we look for new answers in the modern age, I for one prefer the tried and tested recipes, like speaking well of each other and respecting different points of view; coming together to seek out the common ground; and never losing sight of the bigger picture,” the queen said.