There is little you can do in law, if that is your question.
Technically the care home was in breach of contract if you were made, and accepted, the offer of employment. However all they were liable to deliver to you was probably one week of employment, since they could have merely employed you on 30 March but dismissed you on the same day, giving you one's week's minimum notice.
This is appalling state of affairs and they are just keeping you hanging around. You should assume that this job does not exist and be searching for alternative work. Even if it does resurrect itself in the future, I think you should consider very carefully if you really want to work for someone who treats people in this fashion - it would probably be the start of a load of employment hassle anyway. Steer clear.