It may be a private company, large portions of UK (and US I believe) functions are performed by private contractors and have been since the 1980s.
That said, even if it isn't, this experience is something most of us have suffered over the last 15 years from public and private entities. Most have ended up capitulating under pressure to knock it off with the "IE6 only" BS, in part because Microsoft (yes, Microsoft!) forced the issue with IE7 and its follow-ons, itself in part because too many people liked Firefox for Microsoft's comfort.
It shouldn't surprise anyone there's still "IE only" crap out there. Especially amongst organizations that are (1) large, and (2) constantly cutting their budgets and having to apply "defered maintenance" to everything they do to stop going under.
And those budget cuts are, for the most part, the fault of the same people who insist governments are always incompetent.