Unfortunately, the only experience I have with contract employment of that type is first, USA not UK, and second, not recent. My current employment isn't a formal contract because of the added factor of government contract environments. Due to Federal Acquisition Rules for contractor employment, what you describe would be unlikely to happen now.
In a former life, the rule depends on the local, but in essence, failure to agree to a change of employment conditions usually is treated as a resignation unless you can show medical cause to not change hours. I once refused a promotion on medical grounds because of what I would have to do to fulfil the job's travel requirements. Once the company president understood the nature of the problem, he grudgingly accepted the refusal with pretty good grace.
The same company got bought out a couple of years later. The new owners moved a lot of stuff around. I refused to move to another city 1500 miles away and they tried to say that was a resignation. I countered that due to my mother's terminal condition, I couldn't move her and had to stay near her to assure her proper care.
Fortunately, the State of Louisiana had certain exceptions to the labor law that applied at that time. I exercised a medical hardship, which meant that I had not resigned in a normal sense. They had to pay me a severance package. (Which made me feel great because they were a bunch of @$$holes for whom I would not have been happy to work. They later got bought out in turn and lots of the idiots were released. By then I had another job and simply let bygones be long-gones.
Anyway, back to topic - a contract requires "a meeting of the minds." If you don't like the terms they offer, "proper" handing would include a dialog asking why the change occurred and whether there were exceptions or variants available to accomodate folks with scheduling issues, willing to work but unable to meet the new schedule. If you still can't find a meeting of the minds, then there IS no contract.
I would also check the fine print of the old contract to see if it has a "unilateral action" clause in it. If there IS no such clause, they painted themselves into a corner.