Functionally zero. In theory, the monarch has power, but it is never exerted, because they know that if it was exerted a) it would be ignored, and b) they’d immediately be overthrown.

They act as a head of state in the same way that e.g: Germany has a President.

Noble ranks like Duke and Baron are also completely irrelevant to governance.

Lords _are_ relevant, on the other hand. They form the House of Lords, which plays a role as (simplifying) a check on the power of the House of Commons.