Minor point of fact. Before 1982, it was only constitutional changes that had to be okayed by the British Parliament, as the Canadian consitution before that was an act of the U.K. Parliament which could be amended only in Britain (ironically enough, since the U.K. has no written constitution itself). Nowadays, the constitution can be amended in Canada.
All ordinary laws have to be okayed by the Governor-General, who is technically the Queen's representative. (The Queen could do it herself if she had a mind to, but she doesn't bother.) This is no different from pre-1982. The difference is that the G.-G. used to be appointed by the U.K. government, now is appointed by the Canadian government, although technically the Sovereign accepts the appointment.
It's also technically incorrect to say that Canada didn't have a constitution before 1982. The B.N.A. Act *was* a constitution, it just wasn't "patriated". It's now embedded word-for-word in the current constitution, and is equally as lawful as it was before.
I'm sure you're all fascinated by this.