That's not how it works
I'm not sure this is going to form a new Copyright Act or whether it will simply be incorporated into a new copyright treaty (which is the prerogative of the government and does not need any debate).
There have to be three readings of the Bill in both the Commons and the Lords to enact an Act of Parliament. If Parliament is prorogued before the Royal Assent the bill automatically falls and has to start from scratch. There's almost no chance any new copyright bill could pass through these stages, even if both sides were in agreement, before the end of this Parliament.
The first reading is a formality. The government minister (or occasionally a back bencher) announces that a bill on such-and-such is going to be introduced. There's rarely a vote at this point. The real chance to change things is at Second Reading. Here's where all the debate occurs. MPs can post amendments (which must be voted on) or the whole bill can be thrown out.
The bill then goes off to committee for scrutiny (make your own jokes here). The government decides whether to accept the amendments from committee and the bill is then introduced for Third Reading. Usually this is a formality, but the amendments from committee can be voted on. However it's very restrictive and usually guillotined.
If the bill gets to this point it then goes to the Lords for three further readings and a committee stage. The Lords can also suggest amendments or reject the bill. After which it's back to the Commons. Assuming the Lords have no objections the bill goes for Royal Assent. If the Lords have suggested amendments, the government can either choose to accept them or to reject the amendments - at which point, back to the Lords again.
But I suspect, Mandelson's Law, which is fully supported by the Tories will be worded in such a way that any changes to copyright will become law without any public debate.