I'll be honest, I don't think it would come from a politician for risk of someone trying to cry treason.
I suspect if the time comes that it'll be a discussion between politicians and the monarch, and the monarch "voluntarily" stepping down.
It would also need to happen slowly, to allow for the appropriate legislation to pass to remove the ceremonial but necessary legislative role of the monarch - likely the final monarch would sign the legislation ending the monarchy.
There would also be the unraveling of the finances - I know a lot of people like to assume the royals are all fully funded by taxpayers, but that's simply factually incorrect. Even the Sovereign Grant has its complexities as it relates to the Crown Estate, which is neither privately owned by the monarch, nor government property.
Any stepping down of the monarchy would mean establishing what is private wealth and not privy to any disposal unless donated by the monarch/appropriate family member in ownership, what is Crown Estate and how to dispose of this, and whether agreement could be reached as to items or properties that are owned by the monarch outright, but are of significant public interest (the crown jewels spring to mind).
Whenever it comes to pass, I pity the folks involved in the minutiae of it all.