Can't load a specific webpage using Chrome or Safari while logged in, but they work on other account and Firefox also works
So, after an evening of poking at the situation and trying to work out what's going on, I eventually worked it out.

As it transpires, there was an issue with the CRL and OCSP caches on my account on my iMac – other users did not have the same problem as a result. These caches are not deleted by deleting anything from ~/Caches, which is why the issue didn't resolve when I tried that.

The answer came from the Apple Developer Forums, who pointed me to a page on the GlobalSign website. The solution is to open Command Prompt/Terminal and enter one of the following commands, then reboot.

Windows

certutil -urlcache * delete


OS X (pre-Sierra)

sudo rm /var/db/crls/*cache.db


 macOS Sierra

sqlite3 ~/Library/Keychains/*/ocspcache.sqlite3 'DELETE FROM ocsp;'