It seems that the recommended way to change the references to the domain name in MySQL on a WordPress install is to take the whole thing offline and do it by using text tools on a database dump. Either that or change the settings in WordPress while the site is still live on the old domain.
It was too late for the latter and I could not be bothered to do the former – partly because I had just gone through the whole mysql dump routine, partly because the site I wanted to move was only one among a number of sites contained in the dump. While the web server was all set up to use the new domain name, WordPress persisted in redirecting me to the old.
So I looked at the recent database dump, figured out what tables and fields to target so that I could replace the domain name on a live install.