1) Parliamentary Privilege - to search his office is to tear down the very fabric of democracy, you big bullies.
2) You gotta have a warrant - can't search the sacrosanct Houses of Parliament without a warrant, approved by the DPP and blessed by the Archbishop of Canterbury.
Pity about this then:
Parliamentary privilege “does not embrace and protect the activities of individuals, whether members or non-members, simply because they take place within the precincts of Parliament.
and also this:
Section 8 (1) of the Police and Criminal Evidence Act as amended permits a Justice of the Peace to issue a warrant authorising a constable to enter and search premises where satisfied on application by a constable that there are reasonable grounds for believing:[snip]
c) That entry to the premises will not be granted unless a warrant is produced.
So if you think you'll get consent, you don't need a warrant. Why did the police think they'd get consent? Because they asked for it the day before:
On Wednesday 26th November 2008 police officer led by the Senior Investigating Officer attended the Palace of Westminster to speak to the Serjeant at Arms...The officers explained the nature of the investigation and the purpose of the search and were satisfied that the Serjeant at Arms understood that police had no power to search in the absence of a warrant and therefore could only do so with her written consent or that of the Speaker. ... The Serjeant at Arms indicated that she would give her consent at the appropriate time...On the 27th November 2008 officers attended the Palace of Westminster where they again saw the Serjeant at Arms and written consent to search was provided in two forms; namely a signature on a standard police search form 101 and in a letter provided by the Serjeant at Arms. It is understood that the Serjeant at Arms had obtained legal advice in the interim.
It's just like those Stasi pigs to follow the legal requirements. Just thugs in uniform, if you ask me.
(Yes, yes - it's technically possible that the police have published an entirely fictitious account of the crucial events. Wouldn't that be bold.)