Parliamentary privilige, the Bill of Rights 1689, Iain Dale and the statement by Mr Speaker

The events of today, and indeed the past few days over Damian Green strike to the heart of our democracy. Let nobody believe this is a storm in a political tea cup, some bit of trivia. It is wrapped up in the whole basis of our free, representative, parliamentary democracy. But do not let the Tories claim it is about the right to oppose. The fundamentals are about the power of Parliament, not about the government party and opposition - they go back far further in our constitution to that.
Now many are amazed that the Police came without a warrant. And Ian Dale has a posting on this.
But, who could issue such a warrant. The Bill of Rights 1689 says:

That the freedom of speech and debates or proceedings in Parliament ought not to be impeached or questioned in any court or place out of Parliament.

So, in my view, and I am not a lawyer (but this is the sort of issue that if it was commercial law would make lawyers very rich), that the only court that could award such a warrant is the House itself, by calling the police to the bar of the House. Or at least by the House itself delegating that power internally, which is maybe why Mr Speaker said today that he would have final say on future incidents, though I am not convinced that quite fits the relevant section of the Bill of Rights.
Question is, what stipe would issue a warrant to search the offices of a higher court?