Companies are one thing, institutions are quite another. How long do you think it will take the NHS to move on from XP? The procurement process alone will take months, if not years, regardless of how insecure the system may be in the interim. And that's just one, factor in the job centre systems, Immigration, DVLA, HMRC etc. etc. and you're looking at hundreds of systems at a minimum. Probably thousands if not tens of thousands.
It gets funnier when you start thinking about the total costs of doing this. The upgrade to something more secure is comparably cheap compared to the training costs involved in getting who the fuck knows how many people trained on something that isn't what they've been using for X years. I'd guess the training costs are an order of magnitude larger than the upgrade. Which have their own set of procurement processes which will take months, maybe years....
Which makes this a clusterfuck of unknown proportions as you get into the details. Whichever government is eventually formed now gets to deal with both the brexit crap and fallout and a huge list of additional unforeseen expenses at home to try and provide a veneer of security. Which will be inevitably compromised and the whole cycle starts up again.