I thought I’d see if Barclaycard had got their act together at all since yesterday. First, I used the Safari Debug menu (enable it thus; it’s very useful and you can change it back if you want) to masquerade as Internet Explorer 6 on Windows to use the site. Which worked fine – could browse my statement, transactions, and so on.
So then I changed the browser back to “Automatically Chosen”, which should tell the site it’s Mozilla/Safari. And guess what? Works perfectly too.
Either someone had a programming epiphany some time yesterday, or it was a lot simpler to fix than they’d been making out.