Just to bring this to a close, in case anyone else has a similar issue.
The problem was that the GP portal (that provides the package for download after entering work log-in details) gives a version that does not work with Big Sur. Work IT (I am clearly not the first to ask) gave me a link to download a version that does work, in that it asks for the required permissions during installation.
Oddly, when I run GP now, when it opens it says “an older version is available for download, would you like to install it now?”, which I decline.