When does the Monarch Act?

As a republican, I've been through a number of arguments with people about the monarchy. The money is the least of my problems with them. They spend a pittance compared to most of the state, and probably get more back in tourism than that. So, this isn't a post about class war.

I'm more concerned about the constitution of Britain. We don't have a written one with supreme courts or separation into strictly defined parts of government like the USA or France. We have government (which is mostly elected dictatorship for 4 years) and the monarchy. And the monarchy is supposed to uphold the unwritten constitution.

What I'd like to know from people is what they consider the line to be where the monarch steps in and intervenes, and whether they think it could happen. My own view is that removing the right to habeus corpus in some trials was something which probably should have been ruled unconstitutional, the signing of Lisbon after a vote was promised (and not delivered on) and the recent move where the civil service sided against the BNP would also be so.

I would argue that the monarch is achieving little in any of this and I see no purpose in them even existing as a part of government if they aren't going to bother to protect common law. Get rid of them, or get a written constitution and an elected president.