That's like saying, you're all fired but you're welcome to continue with your jobs if you'll take an x% pay-cut.
Can't say I've worked for any company where they're running their affairs that close to the wire to make such a PR-hot-potato/event/policy happen.
[Wasn't something similar done in Detroit, in order to 'break the unions'? You're all fired, but you can re-apply for your jobs outside of the unionisation']
It's nothing to do with UK law as such. The principles of Contract Law are pretty standard, well, within countries that have 1st world legislation. You can't form a contract and then have one side unilaterally alter it's terms. Think of all the scenarios where that could lead...
When you go and open a bank account here, or get a credit card, and so on, there's always lots of smallprint. You always have to tick boxes and sign that you're read and understood it. And if that smallprint changes, they are duty-bound to inform you (rather than assume you review and re-review the smallprint on a daily basis to spot any changes). The flipside (which you seem to be suggesting) is that they could legitimately say double the interest rate charged on your credit card, and not even inform you.
p.s. Did you get out of the wrong side of bed this morning you grump!?
p.s. edit to update.
Ok, your later posts highlight the presence of a contract clause re: a variable pay element. That changes the issue, and hence discussion. If employees sign up to this, then... there you go.