I have left my job anyway, but do I have a claim for constructive dismissal?

You would only have grounds to claim constructive dismissal if you resigned because of your employer's behaviour. You have to show that your employer's conduct was so serious that it amounted to a fundamental breach that went to the heart of the employment contract. 

One example would be making it impossible for you to do your job safely.  

Check your written contract terms carefully. Sometimes, the wording of the employment contract allows your employer to take the action that you object to without your agreement – for example, changing your shift pattern or relocating you to another workplace. 

Your employer cannot be in fundamental breach of the employment contract for doing something the contract expressly allows. Even so, your employer must still obey the implied fundamental duty of mutual trust and confidence. Take advice as soon as possible and talk to your union if you’re a member of one. These are very difficult claims to win. 

Remember also that deadlines for the employment tribunal are extremely short.