It turns out I've been confused about some of this stuff all along. I thought parliaments just ended by themselves.
No. No.
And I thought a session was the period between two Queen's speeches. But no. You were right and I was wrong.
A "session" is the period between the state opening at one end, and prorogation at the other.
Apparently, just as a session has to be formally opened with a Queen's speech, so it also has to be formally closed by prorogation.
Once prorogued, a new session can only start up with a state opening and a Queen's speech.
A new session is begun with a Queen's speech.
Parliament is dissolved at a general election and all seats fall vacant.
After the election, the first session of the new parliament is begun with a Queen's speech