We have an Established Church with the Monarch as Head of the Church of England
It's because we have a collective act of daily worship.
It's because of the role of the C of E in our National Life - Remembrance, Coronation
So I would say it has quite a role in our national life
The full text of the Coronation Oath of King Charles III - Country Life
"Our Majesty, the Church established by law, whose settlement you will swear to maintain, is committed to the true profession of the Gospel, and, in so doing, will seek to foster an environment in which people of all faiths and beliefs may live freely. The Coronation Oath has stood for centuries and is enshrined in law."
Will you to the utmost of your power maintain the Laws of God and the true profession of the Gospel? Will you to the utmost of your power maintain in the United Kingdom the Protestant Reformed Religion established by law? Will you maintain and preserve inviolably the settlement of the Church of England, and the doctrine, worship, discipline, and government thereof, as by law established in England?
And will you preserve unto the Bishops and Clergy of England, and to the Churches there committed to their charge, all such rights and privileges as by law do or shall appertain to them or any of them?
I Charles do solemnly and sincerely in the presence of God profess, testify, and declare that I am a faithful Protestant, and that I will, according to the true intent of the enactments which secure the Protestant succession to the Throne, uphold and maintain the said enactments to the best of my powers according to law.