I would think a unilateral change to the start date, preventing you from starting on the day previously agreed in a contract, would be a breach of contract. But what can you or are you prepared to do about it?
The problem is that even if the employer is not legally allowed to do that, you may in practice be able to do nothing about it. And if they say they want to postpone, you insist on starting on the agreed date and they acquiesce, they could get rid of you one day into your probationary period.
It's best to just get in touch with them and keep in touch on a regular basis. No-one knows what's going to happen, it's a fast moving situation for which the vast majority of employers were not prepared (and some still aren't).
Try not to worry (easier said than done I know) and good luck to you.
[edit]
Just to clarify my edit. In the UK a contract of employment isn't simply the piece of paper with writing and signatures. The employer and employee might have nothing in writing - nevertheless there is a relationship that exists which is governed by law and the agreements (express or implied or inferred) between the two parties.
I am reasonably sure that a start date agreed by email between the two parties would be seen as part of the contract. But, as I suggested, I think that is academic, for even if you could exert the law it wouldn't benefit you to do so. But that is a judgement call for you to make.
You could call ACAS for free but they currently say there are long queues because of the COVID-19 / coronavirus situation.