That is appalling. Someone should be fired for that. If the only way to access your benefits is by running completely unsupported operating systems and browsers that are attached to the Internet, and it doesn't support the majority of users of the site (who on average will be Windows7+ and Chrome or IE8+), then the DWP have demonstrated once again that they simply cannot be trusted to contract out any kind of IT.
Hell - even the DWP won't be able to access the site before the year is out, because they won't be allowed to run XP/IE6 once it leaves extended warranty less than a year from now.
No, that's how outsourcing works.
The contract will included the list of systems to support and the vendor has no obligation to support OS/browser combinations outside the list. Considering this is Win9X-WinXP era production, I can imagine there's many compatibility hack put in the code. To support a newer OS/browser combination, great effort would be needed so the bill would be charged skyhigh.
If it's written by employee, not subcontractors, they'd just point to it and say "Fix it."
They should probably hire someone to rewrite the thing from scratch, and that means we're probably not able to see a new website until one or two years. (Including time loss due to procurement process, (un)expected delay that's common in subcontractors, etc.)