Were there any serious dissenting opinions towards complete sovereignty for Canada and Australia in British politics or society? What about for the Statue of Westminster in 1931 as well?
Hello!
There was no resistance from the Crown for the Canada act in 1982, and official request from the Canadian parliament was passed on quite rapidly and given Royal Assent. Really, the 1982 Act was the logical next step, allowing us to alter our own Constitution without having to consult the British Parliament. This removed a needless and antiquated burden on the British Parliament.
The 1982 act was officially ratified by a signing of HRH Elizabeth II, captured in a very famous image in which the smiling monarch is seen signing the document next to then-PM P. Trudeau. The Photo in question
As for the statute of Westminster, I doubt very much there was any serious dissent, the statue originating from British Parliament itself. The results could only benefit Britain by reducing antiquated logistical strains on her.
Edit: The aforementioned photo, public domain courtesy of the Toronto Star.