Parliament would need a speaker.
It wouldn't need a PM, but it would require a sitting Government... it's also hard to see how any legislation could be passed without a Government either.
I don't know exactly what all the possibilities are, but it seems likely that the PM would try something like this, or perhaps even holding a vote of no confidence in his own Government...
Fair enough, what a mess... guess we'll have to find out what the crack is next week after the Supreme Court ruling? Maybe they'll be back in and back to getting nothing done?